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JEE Area Under Curves PYQs with Solutions

435 previous year questions from Area Under Curves (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

435 questionsMathematics2002–2026Answers + solutions

About Area Under Curves PYQs

Area Under Curves has 435 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (182), JEE Advanced (20) and NTA Abhyas JEE Main (18), spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 18
  • 2025: 20
  • 2024: 24
  • 2023: 29
  • 2022: 21
  • 2021: 19
  • 2020: 29
  • 2019: 15
  • 2018: 5
  • 2017: 3
  • 2016: 3
  • 2015: 2

Area Under Curves questions with solutions

1

Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2 given by y = e^ -x ( x + x) for x ∈ [0, 10π] . Let n be the total number of points of

JEE Advanced 2026 Solution View → 2

Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: If α is the area of the common region that lies inside both the given ellipses, then the

JEE Advanced 2026 Solution View → 3

The area of the region \ (x, y) : x^2 - 8x ≤ y ≤ -x\ is :

JEE Main 2026 Solution View → 4

The area of the region \ (x, y) : 0 ≤ y ≤ 6 - x, y^2 ≥ 4x - 3, x ≥ 0\ is:

JEE Main 2026 Solution View → 5

The area of the region R = \ (x, y): xy ≤ 27, 1 ≤ y ≤ x^2\ is equal to:

JEE Main 2026 Solution View → 6

The area of the region bounded by the curves x+3y^2=0 and x+4y^2=1 is equal to:

JEE Main 2026 Solution View → 7

The area of the region \ (x, y): y ≤ π - |x|, y ≤ |x x|, y ≥ 0\ is:

JEE Main 2026 Solution View → 8

If the area of the region bounded by 16x^2 - 9y^2 = 144 and 8x - 3y = 24 is A, then 3(A + 6 _e(3)) is equal to _______.

JEE Main 2026 Solution View → 9

Let P_ 1 : y=4 x^ 2 and P_ 2 : y=x^ 2 +27 be two parabolas. If the area of the bounded region enclosed between P_ 1 and P_ 2 is six times the area of the bounded region enclosed

JEE Main 2026 Solution View → 10

The area of the region R=\ (x, y): x y ≤ 8,1 ≤ y ≤ x^ 2 , x ≥ 0\ is

JEE Main 2026 Solution View → 11

Let f(α) denote the area of the region in the first quadrant bounded by x=0, x=1, y^ 2 =x and y=|α x-5|-|1-α x|+α x^ 2 . Then (f(0)+f(1)) is equal to

JEE Main 2026 Solution View → 12

Let A_ 1 be the bounded area enclosed by the curves y=x^ 2 +2, x+y=8 and y -axis that lies in the first quadrant. Let A_ 2 be the bounded area enclosed by the curves y=x^ 2 +2, y^

JEE Main 2026 Solution View → 13

The area of the region enclosed between the circles x^ 2 +y^ 2 =4 and x^ 2 +(y-2)^ 2 =4 is:

JEE Main 2026 Solution View → 14

Let the area of the region bounded by the curve y= \ x, x\ , lines x=0, x=(3 π)/(2) , and the x -axis be A. Then, A+A^ 2 is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 15

The area of the region A=\ (x, y): 4 x^ 2 +y^ 2 8. and .y^ 2 4 x\ is:

JEE Main 2026 Solution View → 16

Let the line x=-1 divide the area of the region \ (x, y): 1+x^ 2 ≤ y ≤ 3-x\ in the ratio m: n, gcd(m, n)=1 . Then m+n is equal to

JEE Main 2026 Solution View → 17

If the area of the region \ (x, y): 1-2 x y 4-x^ 2 , x 0, y 0\ is (α)/(β), α, β ∈ N, gcd(α, β)=1 , then the value of (α+β) is :

JEE Main 2026 Solution View → 18

The area of the region, inside the ellipse x^ 2 +4 y^ 2 =4 and outside the region bounded by the curves y=|x|-1 and y=1-|x| , is :

JEE Main 2026 Solution View → 19

Let ℝ denote the set of all real numbers. Then the area of the region \ (x, y) ∈ ℝ × ℝ: x>0, y>(1)/(x), 5 x-4 y-1>0,4 x+4 y-17 <0\ is

JEE Advanced 2025 Solution View → 20

Let the area of the bounded region \ (x, y): 0 ≤ 9 x ≤ y^2, y ≥ 3 x-6\ be A. Then 6 A is equal to ________

JEE Main 2025 Solution View → 21

If the area of the region \ (x, y): 1+x^2 ≤ y ≤ \ x+7,11-3 x\ \ is A , then 3 A is equal to

JEE Main 2025 Solution View → 22

If the area of the region bounded by the curves \(y=4- (x^2)/(4) \) and \(y= (x-4)/(2) \) is equal to \( α \), then \(6 α \) equals

JEE Main 2025 Solution View → 23

If the area of the region \ (x, y):|x-5| ≤ y ≤ 4 x \ is A , then 3 A is equal to _____ .

JEE Main 2025 Solution View → 24

The area of the region \ (x, y):|x-y| ≤ y ≤ 4 x \ is

JEE Main 2025 Solution View → 25

The area of the region bounded by the curve y= \ |x|, x|x-2|\ , then x -axis and the lines x=-2 and x=4 is equal to _______ .

JEE Main 2025 Solution View → 26

If the area of the region \ (x, y):|4-x^2| ≤ y ≤ x^2, y ≤ 4, x ≥ 0\ is ( 80 2 α -β), α , β ∈ N, then α+β is equal to _______.

JEE Main 2025 Solution View → 27

Let the area enclosed between the curves |y|=1-x^2 and x^2+y^2=1 be α . If 9 α=β π+γ ; β, γ are integers, then the value of |β-γ| equals.

JEE Main 2025 Solution View → 28

Let the area of the region \(\ (x, y): 2 y ≤ x^2+3, y+|x| ≤ 3, y |x-1|\ \) be A. Then 6 A is equal to :

JEE Main 2025 Solution View → 29

The area of the region bounded by the curves x(1+y^2)=1 and y^2=2 x is:

JEE Main 2025 Solution View → 30

The area (in sq. units) of the region \ (x, y): 0 ≤ y ≤ 2|x|+1,0 ≤ y ≤ x^2+1,|x| ≤ 3\ is

JEE Main 2025 Solution View → 31

The area of the region enclosed by the curves y=e^x, y=|e^x-1| and y -axis is:

JEE Main 2025 Solution View → 32

The area of the region \ (x, y): x^2+4 x+2 ≤ y ≤|x+2|\ is equal to

JEE Main 2025 Solution View → 33

Consider the region R=\ (x, y): x ≤ y ≤ 9-(11)/(3) x^2, x ≥ 0\ . The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:

JEE Main 2025 Solution View → 34

If the area of the region \ (x, y):-1 ≤ x ≤ 1,0 ≤ y ≤ a+e^ |x| -e^ -x , a 0\ is e^2+8 e+1 e , then the value of a is :

JEE Main 2025 Solution View → 35

If the area of the larger portion bounded between the curves x^2+y^2=25 and y=|x-1| is (1)/(4)(b π+c), b, c ∈ N , then b+c is equal to

JEE Main 2025 Solution View → 36

The area of the region enclosed by the curves y=x^2-4 x+4 and y^2=16-8 x is :

JEE Main 2025 Solution View → 37

Let f: R arrow R be a twice differentiable function such that f(x+y)=f(x) f(y) for all x, y ∈ R . If f^ (0)=4 a and f satisfies f^ (x)-3 a f^ (x)-f(x)=0 , a 0 , then the area of

JEE Main 2025 Solution View → 38

The area of the region, inside the circle (x-2 3 )^2+y^2=12 and outside the parabola y^2=2 3 x is :

JEE Main 2025 Solution View → 39

Let S=\ (x, y) ∈ ℝ × ℝ: x ≥ 0, y ≥ 0, y^2 ≤ 4 x, y^2 ≤ 12-2 x. and .3 y+ 8 x ≤ 5 8 \ . If the area of the region S is α 2 , then α is equal to

JEE Advanced 2024 Solution View → 40

The area (in square units) of the region enclosed by the ellipse x^2+3 y^2=18 in the first quadrant below the line y=x is

JEE Main 2024 Solution View → 41

The parabola y^2=4 x divides the area of the circle x^2+y^2=5 in two parts. The area of the smaller part is equal to:

JEE Main 2024 Solution View → 42

The area of the region in the first quadrant inside the circle x^2+y^2=8 and outside the parabola y^2=2 x is equal to :

JEE Main 2024 Solution View → 43

Let f(x) be a positive function such that the area bounded by y=f(x), y=0 from x=0 to x=a>0 is e^ -a +4 a^2+a-1 . Then the differential equation, whose general solution is y=c_1

JEE Main 2024 Solution View → 44

Let the area of the region enclosed by the curve y= \ x, x\ and the x axis between x=-π to x=π be A . Then A^2 is equal to ___________

JEE Main 2024 Solution View → 45

If the area of the region \ (x, y): a x^2 ≤ y ≤ (1)/(x), 1 ≤ x ≤ 2,0 < a < 1\ is ( _ e 2)-(1)/(7) then the value of 7 a-3 is equal to:

JEE Main 2024 Solution View → 46

Let the area of the region enclosed by the curves y=3 x, 2 y=27-3 x and y=3 x-x x be A . Then 10 A is equal to

JEE Main 2024 Solution View → 47

The area enclosed between the curves y=x|x| and y=x-|x| is :

JEE Main 2024 Solution View → 48

The area of the region enclosed by the parabolas y=x^2-5 x and y=7 x-x^2 is

JEE Main 2024 Solution View → 49

The area (in sq. units) of the region described by \ (x, y): y^2 ≤ 2 x. , and .y ≥ 4 x-1\ is

JEE Main 2024 Solution View → 50

One of the points of intersection of the curves y=1+3 x-2 x^2 and y=(1)/(x) is ((1)/(2), 2) . Let the area of the region enclosed by these curves be (1)/(24)(l 5 +m)-n _ e (1+ 5 )

JEE Main 2024 Solution View → 51

Three points O(0, 0), P(a, a ^ 2 ), Q(- b, b ^ 2 ), a > 0, b > 0, are on the parabola y = x ^ 2 . Let S _ 1 be the area of the region bounded by the line PQ and the parabola, and

JEE Main 2024 Solution View → 52

The sum of squares of all possible values of k , for which area of the region bounded by the parabolas 2 y ^ 2 = kx and k y ^ 2 = 2(y - x) is maximum, is equal to:

JEE Main 2024 Solution View → 53

The area enclosed by the curves xy + 4y = 16 and x + y = 6 is equal to:

JEE Main 2024 Solution View → 54

The area of the region enclosed by the parabola y = 4x - x ^ 2 and 3y = (x - 4) ^ 2 is equal to

JEE Main 2024 Solution View → 55

The area of the region \ (x, y): y ^ 2 ≤ 4x, x < 4, (xy(x - 1)(x - 2))/((x - 3)(x - 4)) > 0, x ≠ 3\ is

JEE Main 2024 Solution View → 56

The area of the region enclosed by the parabola ( y - 2 ) ^ 2 = x - 1 , the line x - 2y + 4 = 0 and the positive coordinate axes is __________.

JEE Main 2024 Solution View → 57

Let Y = Y ( X ) be a curve lying in the first quadrant such that the area enclosed by the line Y - y = Y ^ ' ( x ) ( X - x ) and the co-ordinate axes, where ( x, y ) is any point

JEE Main 2024 Solution View → 58

The area (in square units) of the region bounded by the parabola y ^ 2 = 4 ( x - 2 ) and the line y = 2x - 8 .

JEE Main 2024 Solution View → 59

Let the area of the region ( x, y ) : 0 ≤ x ≤ 3, 0 ≤ y ≤ min \ x ^ 2 + 2, 2x + 2\ \ be A . Then 12A is equal to ______.

JEE Main 2024 Solution View → 60

The area (in sq. units) of the part of circle x ^ 2 + y ^ 2 = 169 which is below the line 5x - y = 13 is (πα)/(2β) - (65)/(2) + (α)/(β) ^ - 1 ((12)/(13)) where α, β are coprime

JEE Main 2024 Solution View → 61

If the area of the region \ ( x, y ) : 0 ≤ y ≤ min \ 2x, 6x - x ^ 2 \ \ is A , then 12A is equal to _______.

JEE Main 2024 Solution View → 62

Let the area of the region ( x, y ) : x - 2y + 4 ≥ 0 , x + 2 y ^ 2 ≥ 0, x + 4 y ^ 2 ≤ 8, y ≥ 0\ be (m)/(n) , where m and n are coprime numbers. Then m + n is equal to ______.

JEE Main 2024 Solution View → 63

Let f: [0, 1] → [0, 1] be the function defined by f(x) = x ^ 3 3 - x ^ 2 + (5)/(9)x + (17)/(36) . Consider the square region S = [0, 1] × [0, 1] . Let G = \ (x, y) ∈ S: y > f(x)\

JEE Advanced 2023 Solution View → 64

Let n ≥ 2 be a natural number and f: [0, 1] → ℝ be the function defined by f(x) = \ cases n(1 - 2nx) & if & 0 ≤ x ≤ (1)/(2n) 2n(2nx - 1) & if & (1)/(2n) ≤ x ≤ (3)/(4n) 4n(1 - nx)

JEE Advanced 2023 Solution View → 65

If the area bounded by the curve 2 y ^ 2 = 3x , lines x + y = 3, y = 0 and outside the circle (x - 3) ^ 2 + y ^ 2 = 2 is A, then 4(π + 4A) is equal to __________.

JEE Main 2023 Solution View → 66

The area of the region x, y: x ^ 2 ≤ y ≤ | x ^ 2 - 4|, y ≥ 1 is

JEE Main 2023 Solution View → 67

The area of the region enclosed by the curve f(x) = max sinx, cosx , - π ≤ x ≤ π and the x - axis is

JEE Main 2023 Solution View → 68

The area of the region enclosed by the curve y = x ^ 3 and its tangent at the point ( – 1, – 1 ) is

JEE Main 2023 Solution View → 69

If A is the area in the first quadrant enclosed by the curve C: 2 x ^ 2 - y + 1 = 0 , the tangent to C at the point (1, 3) and the line x + y = 1 , then the value of 60A

JEE Main 2023 Solution View → 70

Area of the region \ (x, y) : x ^ 2 + (y - 2) ^ 2 ≤ 4, x ^ 2 ≥ 2y\ is

JEE Main 2023 Solution View → 71

If the area of the region \ (x, y): | x ^ 2 - 2| ≤ y ≤ x\ is A , then 6A + 16 2 is equal to ______________

JEE Main 2023 Solution View → 72

Let y = p(x) be the parabola passing through the points (– 1, 0), (0, 1) and (1, 0) . If the area of the region \ (x, y): (x + 1) ^ 2 + (y - 1) ^ 2 ≤ 1, y ≤ p(x)\ is A , then 12(π

JEE Main 2023 Solution View → 73

Let the area enclosed by the lines x + y = 2, y = 0 , x = 0 and the curve f ( x ) = min\ x ^ 2 + (3)/(4), 1 + [ x ]\ where [ x ] denotes the greatest integer ≤ x , be A . Then the

JEE Main 2023 Solution View → 74

The area of the region \ (x, y) : x ^ 2 ≤ y ≤ 8 - x ^ 2 , y ≤ 7\ is

JEE Main 2023 Solution View → 75

The area bounded by the curves y = |x - 1| + |x - 2| and y = 3 is equal to

JEE Main 2023 Solution View → 76

If the area of the region S = \ ( x, y ) : 2y - y ^ 2 ≤ x ^ 2 ≤ 2y, x ≥ y\ is equal to (n + 2)/(n + 1) - (π)/(n - 1), then the natural number n is equal to _______

JEE Main 2023 Solution View → 77

The area of the region given by \ (x, y) : xy ≤ 8, 1 ≤ y ≤ x ^ 2 \ is :

JEE Main 2023 Solution View → 78

The area enclosed by the closed curve C given by the differential equation (dy)/(dx) + (x + a)/(y - 2) = 0, y(1) = 0 is 4π . Let P and Q be the points of intersection of the curve

JEE Main 2023 Solution View → 79

Let A be the area bounded by the curve y = x|x - 3| , the x -axis and the ordinates x = - 1 and x = 2 . Then 12A is equal to _____ .

JEE Main 2023 Solution View → 80

Let the area of the region \ (x, y): |2x - 1| ≤ y ≤ | x ^ 2 - x|, 0 ≤ x ≤ 1\ be A . Then (6A + 11) ^ 2 is equal to _____ .

JEE Main 2023 Solution View → 81

Let for x ∈ R , f(x) = (x + |x|)/(2) and g(x) = \ array ll x, x ^ 2 , array array ll x < 0 x ≥ 0 array ). Then area bounded by the curve y = (fog)(x) and the lines y = 0, 2y - x =

JEE Main 2023 Solution View → 82

Let q be the maximum integral value of p in [0, 10] for which the roots of the equation x ^ 2 - px + (5)/(4)p = 0 are rational. Then the area of the region \ (x, y): 0 ≤ y ≤ ( x

JEE Main 2023 Solution View → 83

Let A be the area of the region \ ( x, y ) : y ≥ x ^ 2 , y ≥ ( 1 - x ) ^ 2 , y ≤ 2x ( 1 - x )\ . Then 540A is equal to

JEE Main 2023 Solution View → 84

Let α be the area of the larger region bounded by the curve y ^ 2 = 8x and the lines y = x and x = 2 , which lies in the first quadrant. Then the value of 3α is equal to

JEE Main 2023 Solution View → 85

The area of the region A = \ (x, y): |cosx - sinx| ≤ y ≤ sinx, 0 ≤ x ≤ (π)/(2)\

JEE Main 2023 Solution View → 86

Let A = \ (x, y) ∈ ℝ ^ 2 : y ≥ 0, 2x ≤ y ≤ 4 - (x - 1) ^ 2 \ and B = \ (x, y) ∈ ℝ × ℝ: 0 ≤ y ≤ min\ 2x, 4 - (x - 1) ^ 2 \ \ . Then the ratio of the area of A to the area of B is

JEE Main 2023 Solution View → 87

Let Δ be the area of the region \ (x, y) ∈ ℝ ^ 2 : x ^ 2 + y ^ 2 ≤ 21, y ^ 2 ≤ 4x, x ≥ 1\ . Then (1)/(2)(Δ - 21 ^ - 1 2 7 ) is equal to

JEE Main 2023 Solution View → 88

Let T and C respectively, be the transverse and conjugate axes of the hyperbola 16 x ^ 2 - y ^ 2 + 64x + 4y + 44 = 0 . Then the area of the region above the parabola x ^ 2 = y + 4

JEE Main 2023 Solution View → 89

If the area enclosed by the parabolas P _ 1 : 2y = 5 x ^ 2 and P _ 2 : x ^ 2 - y + 6 = 0 is equal to the area enclosed by P _ 1 and y = , α > 0 , then α ^ 3 is equal to _____ .

JEE Main 2023 Solution View → 90

If the area of the region bounded by the curves y ^ 2 - 2y = - x and x + y = 0 is A , then 8A =

JEE Main 2023 Solution View → 91

The area enclosed between the curves y ^ 2 + 4x = 4 and y - 2x = 2 is

JEE Main 2023 Solution View → 92

Consider the functions f, g: ℝ → ℝ defined by f(x) = x ^ 2 + (5)/(12) and g(x) = \ cases 2(1 - (4|x|)/(3)), & |x| ≤ (3)/(4), 0, & |x| > (3)/(4) cases ) If α is the area of the

JEE Advanced 2022 Solution View → 93

The area of the region \ (x, y): |x - 1| ≤ y ≤ 5 - x ^ 2 \ is equal to

JEE Main 2022 Solution View → 94

The area enclosed by the curves y = _ e (x + e ^ 2 ), x = _ e ((2)/(y)) and x = _ e 2 , above the line y = 1 is

JEE Main 2022 Solution View → 95

The area of the region enclosed by y ≤ 4 x ^ 2 , x ^ 2 ≤ 9y and y ≤ 4 , is equal to

JEE Main 2022 Solution View → 96

Consider a curve y = y(x) in the first quadrant as shown in the figure. Let the area A _ 1 is twice the area A _ 2 . Then the normal to the curve perpendicular to the line 2x

JEE Main 2022 Solution View → 97

The area of the smaller region enclosed by the curves y ^ 2 = 8x + 4 and x ^ 2 + y ^ 2 + 4 3 x - 4 = 0 is equal to

JEE Main 2022 Solution View → 98

The area bounded by the curves y = | x ^ 2 - 1| and y = 1 is

JEE Main 2022 Solution View → 99

The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = y ^ a is (364)/(3) , equal to:

JEE Main 2022 Solution View → 100

Let a curve y = y(x) pass through the point (3, 3) and the area of the region under this curve, above the x -axis and between the abscissae 3 and x (> 3) be ((y)/(x)) ^ 3 . If

JEE Main 2022 Solution View → 101

The area of the region given by A = \ (x, y): x ^ 2 ≤ y ≤ min\ x + 2, 4 - 3x\ \ is

JEE Main 2022 Solution View → 102

For real numbers a, b(a > b > 0) , let Area \ (x, y): x ^ 2 + y ^ 2 ≤ a ^ 2 ) and x ^ 2 a ^ 2 + y ^ 2 b ^ 2 ≥ 1\ = 30π and Area \ (x, y): x ^ 2 + y ^ 2 ≥ b ^ 2 ) and x ^ 2 a ^ 2 +

JEE Main 2022 Solution View → 103

The area enclosed by y ^ 2 = 8x and y = 2 x that lies outside the triangle formed by y = 2 x, x = 1, y = 2 2 , is equal to

JEE Main 2022 Solution View → 104

The area of the bounded region enclosed by the curve y = 3 - |x - (1)/(2)| - |x + 1| and the x -axis is

JEE Main 2022 Solution View → 105

The area of the region S = \ (x, y): y ^ 2 ≤ 8x, y ≥ 2 x, x ≥ 1\ is

JEE Main 2022 Solution View → 106

If the area of the region \ (x, y): x(2)/(3) +y(2)/(3) ≤ 1, x + y ≥ 0, y ≥ 0\ is A , then (256A)/(π) is

JEE Main 2022 Solution View → 107

Let A _ 1 = \ (x, y): |x| ≤ y ^ 2 , |x| + 2y ≤ 8\ and A _ 2 = \ (x, y): |x| + |y| ≤ k\ . If 27 (Area A _ 1 ) = 5 (Area A _ 2 ), then k is equal to

JEE Main 2022 Solution View → 108

The area of the region bounded by y ^ 2 = 8x and y ^ 2 = 16(3 - x) is equal to

JEE Main 2022 Solution View → 109

The area bounded by the curve y = | x ^ 2 - 9| and the line y = 3 is

JEE Main 2022 Solution View → 110

The area of the region enclosed between the parabolas y ^ 2 = 2x - 1 and y ^ 2 = 4x - 3 is.

JEE Main 2022 Solution View → 111

The area (in sq. units) of the region enclosed between the parabola y ^ 2 = 2x and the line x + y = 4 is ______.

JEE Main 2022 Solution View → 112

Let S be the region bounded by the curves y = x ^ 3 and y ^ 2 = x . The curve y = 2|x| divides S into two regions of areas R _ 1 and R _ 2 . If max| R _ 1 , R _ 2 | = R _ 2 , then

JEE Main 2022 Solution View → 113

The area of the region \ ( x, y ) : 0 ≤ x ≤ (9)/(4), 0 ≤ y ≤ 1, x ≥ 3y, x + y ≥ 2\ is

JEE Advanced 2021 Solution View → 114

The area, enclosed by the curves y = sinx + cosx and y = | cosx - sinx | and the lines x = 0, x = (π)/(2), is :

JEE Main 2021 Solution View → 115

If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = (3)/(2) and the curve y = 1 + 4x - x ^ 2 , then 12m is equal to .

JEE Main 2021 Solution View → 116

The area of the region bounded by the parabola ( y - 2 ) ^ 2 = ( x - 1 ) , the tangent to it at the point whose ordinate is 3 and the x -axis, is:

JEE Main 2021 Solution View → 117

Let a and b respectively be the points of local maximum and local minimum of the function f ( x ) = 2 x ^ 3 - 3 x ^ 2 - 12x . If A is the total area of the region bounded by y = f

JEE Main 2021 Solution View → 118

The area of the region S = \ ( x, y ) : 3 x ^ 2 ≤ 4y ≤ 6x + 24\ is______.

JEE Main 2021 Solution View → 119

The area of the region bounded by y - x = 2 and x ^ 2 = y is equal to :-

JEE Main 2021 Solution View → 120

If the area of the bounded region R = \ (x, y): max\ 0, _ e x\ ≤ y ≤ 2 ^ x , (1)/(2) ≤ x ≤ 2\ is, α ( _ e 2) ^ - 1 + β( _ e 2) + γ then the value of (α + β - 2γ) ^ 2 is equal to:

JEE Main 2021 Solution View → 121

The area (in sq. units) of the region, given by the set \ (x, y) ∈ R × R ∣ x ≥ 0, 2 x ^ 2 ≤ y ≤ 4 - 2x\ is :

JEE Main 2021 Solution View → 122

The area (in sq. units) of the region bounded by the curves x ^ 2 + 2y - 1 = 0, y ^ 2 + 4x - 4 = 0 and y ^ 2 - 4x - 4 = 0 in the upper half plane is _________.

JEE Main 2021 Solution View → 123

Let T be the tangent to the ellipse E: x ^ 2 + 4 y ^ 2 = 5 at the point P ( 1, 1 ) . If the area of the region bounded by the tangent T , ellipse E , lines x = 1 and x = 5 is α 5

JEE Main 2021 Solution View → 124

The area (in sq. unit) bounded by the curve 4 y ^ 2 = x ^ 2 ( 4 - x ) ( x - 2 ) is equal to

JEE Main 2021 Solution View → 125

Let f: [ - 3, 1 ] → R be given as f(x) = \ cases min\ ( x + 6 ) , x ^ 2 \ , & - 3 ≤ x ≤ 0 max\ x , x ^ 2 \ , & 0 ≤ x ≤ 1 cases .)If the area bounded by y = f ( x ) and x -axis is

JEE Main 2021 Solution View → 126

Let the curve y = y(x) be the solution of the differential equation, (dy)/(dx) = 2(x + 1) . If the numerical value of area bounded by the curve y = y(x) and x -axis is 4 8 3

JEE Main 2021 Solution View → 127

Let A _ 1 be the area of the region bounded by the curves y = sinx, y = cosx and y -axis in the first quadrant. Also, let A _ 2 be the area of the region bounded by the curves y =

JEE Main 2021 Solution View → 128

The area bounded by the lines y = ||x - 1| - 2| and y=2 is _____.

JEE Main 2021 Solution View → 129

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A .

JEE Main 2021 Solution View → 130

The area of the region: R = \ (x, y): 5 x ^ 2 ≤ y ≤ 2 x ^ 2 + 9\ is

JEE Main 2021 Solution View → 131

The area (in sq. units) of the part of the circle x ^ 2 + y ^ 2 = 36 , which is outside the parabola y ^ 2 = 9x , is equal to

JEE Main 2021 Solution View → 132

Let the functions f: R → R and g: R → R be defined by f(x) = e ^ x - 1 - e ^ - |x - 1| and g(x) = (1)/(2)( e ^ x - 1 + e ^ 1 - x ) . Then the area of the region in the first

JEE Advanced 2020 Solution View → 133

The area (in sq. units) of the region enclosed by the curves y = x ^ 2 - 1 and y = 1 - x ^ 2 is equal to:

JEE Main 2020 Solution View → 134

The area (in sq. units) of the region A = \ ( x, y ) : | x | + | y | ≤ 1, 2 y ^ 2 ≥ | x |\

JEE Main 2020 Solution View → 135

The area (in sq. units) of the region A = ( x, y ) : ( x - 1 ) [ x ] ≤ y ≤ 2 x , 0 ≤ x ≤ 2 , where [ t ] denotes the greatest integer function, is :

JEE Main 2020 Solution View → 136

The area (in sq. units) of the region \ (x, y) : 0 ≤ y ≤ x ^ 2 + 1, 0 ≤ y ≤ x + 1, (1)/(2) ≤ x ≤ 2\ is

JEE Main 2020 Solution View → 137

Consider a region R = \ (x, y) ∈ R ^ 2 : x ^ 2 ≤ y ≤ 2x\ . If a line y = α divides the area of region R into two equal parts, then which of the following is true ?

JEE Main 2020 Solution View → 138

Area (in sq. units) of the region outside (|x|)/(2) + (|y|)/(3) = 1 and inside the ellipse x ^ 2 4 + y ^ 2 9 = 1 is

JEE Main 2020 Solution View → 139

Given: f(x) = \ array ll x, 0 ≤ x (1)/(2), x = (1)/(2) array 1 - x, (1)/(2)) and g(x) = (x - (1)/(2)) ^ 2 , x ∈ R . Then, the area (in sq. units) of the region bounded by the

JEE Main 2020 Solution View → 140

The area (in sq. units) of the region \ (x, y) ∈ R ^ 2 : x ^ 2 ≤ y ≤ 3 - 2x\ , is.

JEE Main 2020 Solution View → 141

The area (in sq. units) of the region \ (x, y) ∈ R ^ 2 |4 x ^ 2 ≤ y ≤ 8x + 12\ is

JEE Main 2020 Solution View → 142

The area of the region (in sq. units), enclosed by the circle x ^ 2 + y ^ 2 = 2 which is not common to the region bounded by the parabola y ^ 2 = x and the straight line y = x , is

JEE Main 2020 Solution View → 143

The area bounded by the curves y = (x - 1) ^ 2 , y = (x + 1) ^ 2 and y = (1)/(4) is

NTA Abhyas JEE Main 2020 Solution View → 144

A farmer F _ 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From this land, a neighbouring farmer F _ 2 takes away the region

NTA Abhyas JEE Main 2020 Solution View → 145

The area bounded by y = xe^ |x| and the lines |x| = 1, y = 0 is

NTA Abhyas JEE Main 2020 Solution View → 146

The area bounded by the curve y = (1)/(2)x^ 2 , x -axis and x = 2 is

NTA Abhyas JEE Main 2020 Solution View → 147

The area between the curve y = 2x^ 4 - x^ 2 , the x -axis and the ordinates of the two minima of the curve is

NTA Abhyas JEE Main 2020 Solution View → 148

The area bounded by the curves y = x^ 2 and y = 2 (1 + x^ 2 ) is

NTA Abhyas JEE Main 2020 Solution View → 149

The value of the parameter ‘a' such that the area bounded by y = a^ 2 x^ 2 + ax + 1 , coordinate axes and the line x = 1 attains its least value, is equal to

NTA Abhyas JEE Main 2020 Solution View → 150

The positive value of parameter a for which the area bounded by parabolas y = x - a x ^ 2 and ay = x ^ 2 attains the maximum value is

NTA Abhyas JEE Main 2020 Solution View → 151

The area enclosed between the curves y = ax ^ 2 and x = ay ^ 2 (a > 0) is 1 sq unit. If the value of a is 3 3 λ , then the value of λ is

NTA Abhyas JEE Main 2020 Solution View → 152

The area of the region (in square units) above the x -axis bounded by the curve y ⁡ = ,0 ≤ x ⁡ ≤ (π)/(2) and the tangent to the curve at x ⁡ = (π)/(4) & is&

NTA Abhyas JEE Main 2020 Solution View → 153

The area (in square units) enclosed by& |y| - |x| = 1 and x^ 2 + y^ 2 = 1 is

NTA Abhyas JEE Main 2020 Solution View → 154

The area bounded by the curves y = x , y = |x| , y = | x| and y = | |x|| , for x ∈ ( - 1, 1 ) is

NTA Abhyas JEE Main 2020 Solution View → 155

The parabolas y^ 2 = 4x and x^ 2 = 4y divide the square region bounded by the lines x = 4 , y = 4 and the coordinate axes. If S _ 1 , S _ 2 , S _ 3 are respectively the areas of

NTA Abhyas JEE Main 2020 Solution View → 156

The area of the closed region bounded by y = ^ -1 ⁡ x, y = cosec^ - 1 x and the line x - 1 = 0 is

NTA Abhyas JEE Main 2020 Solution View → 157

The area bounded by the graph y = | [x - 3]| , above the x -axis from x = - 2 to x = 3 is ([.] denotes the greatest integer function)

NTA Abhyas JEE Main 2020 Solution View → 158

The area (in sq. units) bounded by the curve f(x) = \ cases e^ - |x| & |x| ≥ 1 |x| - 1 + (1)/(e)& |x| < 1 cases ) and the x -axis is

NTA Abhyas JEE Main 2020 Solution View → 159

The area bounded by the curve y^ 2 = 1 - x and the lines y = (|x|)/(x), x = - 1 and x = (1)/(2) is

NTA Abhyas JEE Main 2020 Solution View → 160

The area (in sq. units) of the region (x, y): y^ 2 ≥ 2x and x^ 2 + y^ 2 ≤ 4x, x ≥ 0, y ≥ 0 is

NTA Abhyas JEE Main 2020 Solution View → 161

The area of the region \ (x, y) : xy ≤ 8, 1 ≤ y ≤ x ^ 2 \ is

JEE Advanced 2019 Solution View → 162

If the area (in sq. units) bounded by the parabola y ^ 2 = 4 and the line y = , λ > 0, is (1)/(9) , then λ is equal to

JEE Main 2019 Solution View → 163

If the area (in sq. units) of the region \ (x, y) : y ^ 2 ≤ 4x, x + y ≤ 1, x ≥ 0, y ≥ 0\ is a 2 + b, then a - b is equal to

JEE Main 2019 Solution View → 164

The area (in sq. units) of the region bounded by the curves y = 2 ^ x and y = |x + 1| , in the first quadrant is

JEE Main 2019 Solution View → 165

The region represented by |x - y| ≤ 2 and |x + y| ≤ 2 is bounded by a

JEE Main 2019 Solution View → 166

The area (in sq. units) of the region A = \ (x, y): y ^ 2 2 ≤ x ≤ y + 4\ is:

JEE Main 2019 Solution View → 167

The area (in sq. units) of the region A = \ (x, y): x ^ 2 ≤ y ≤ x + 2\ is

JEE Main 2019 Solution View → 168

Let S(α) = \ (x, y): y ^ 2 ≤ x, 0 ≤ x ≤ α\ and A(α) is area of the region S(α) . If for a λ, 0 < λ < 4, A(λ): A(4) = 2: 5, then λ equals:

JEE Main 2019 Solution View → 169

The area (in sq. units) of the region A = \ (x, y) ∈ R × R0 ≤ x ≤ 3, 0 ≤ y ≤ 4, y ≤ x ^ 2 + 3x\ is

JEE Main 2019 Solution View → 170

The area (in sq. units) of the region bounded by the parabola, y = x ^ 2 + 2 and the lines, y = x + 1, x = 0 and x = 3 , is

JEE Main 2019 Solution View → 171

The area (in sq. units) in the first quadrant bounded by the parabola, y=x^ 2 +1 , the tangent to it at the point (2,5) and the coordinate axes is :

JEE Main 2019 Solution View → 172

The area (in sq. units) of the region bounded by the curve x^ 2 =4 y and the straight line x=4 y-2 is :

JEE Main 2019 Solution View → 173

If the area enclosed between the curves y = k x ^ 2 and x = k y ^ 2 , (k > 0), is 1sq . unit . Then k is

JEE Main 2019 Solution View → 174

The area of the region A = (x, y): 0 ≤ y ≤ x|x| + 1and - 1 ≤ x ≤ 1 in sq. units, is

JEE Main 2019 Solution View → 175

The area (in sq. units) bounded by the parabola y = x ^ 2 - 1, the tangent at the point (2, 3) to it and the y -axis is

JEE Main 2019 Solution View → 176

A farmer F _ 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From this land, a neighbouring farmer F _ 2 takes away the region

JEE Advanced 2018 Solution View → 177

If the area of the region bounded by the curves, y = x ^ 2 , y = (1)/(x) and the lines y = 0 and x = t(t > 1) is 1sq . unit , then t is equal to

JEE Main 2018 Solution View → 178

The area (in sq. units) of the region \ x ∈ R: x ≥ 0, y ≥ 0, y ≥ x-2 and y ≤ x \ , is

JEE Main 2018 Solution View → 179

The area (in sq. units) of the region x ∈ R: x ≥ 0, y ≥ 0, y ≥ x - 2 and y ≤ x is

JEE Main 2018 Solution View → 180

Let g(x) = cos x ^ 2 , f(x) = x , and α, β(α < β) be the roots of the quadratic equation 18 x ^ 2 - 9 + π ^ 2 = 0 . Then the area (in sq. units) bounded by the curve y = (gof)(x)

JEE Main 2018 Solution View → 181

If the line x = α divides the area of the region R = (x, y) ∈ R ^ 2 : x ^ 3 ≤ y ≤ x, 0 ≤ x ≤ 1 into two equal parts, then

JEE Advanced 2017 Solution View → 182

The area (in sq. units) of the smaller portion enclosed between the curves, x ^ 2 + y ^ 2 = 4 and y ^ 2 = 3x , is:

JEE Main 2017 Solution View → 183

The area (in sq. units) of the region \ (x, y) : x ≥ 0, x + y ≤ 3, x ^ 2 ≤ 4yandy ≤ 1 + x \ is

JEE Main 2017 Solution View → 184

Area of the region (x, y) ∈ R ^ 2 : y ≥ |x + 3| , 5y ≤ x + 9 ≤ 15 is equal to

JEE Advanced 2016 Solution View → 185

The area (in sq. units) of the region described by A = \ (x, y) | y ≥ x ^ 2 - 5x + 4, x + y ≥ 1, y ≤ 0\ is

JEE Main 2016 Solution View → 186

The area (in sq . units ) of the region (x, y): y ^ 2 ≥ 2x and x ^ 2 + y ^ 2 ≤ 4x, x ≥ 0, y ≥ 0 is

JEE Main 2016 Solution View → 187

The area (in square units) of the region bounded by the curves y + 2 x ^ 2 = 0 and y + 3 x ^ 2 = 1 , is equal to

JEE Main 2015 Solution View → 188

The area (in sq. units) of the region described by [(x, y) : y ^ 2 ≤ 2xandy ≥ 4x - 1] is

JEE Main 2015 Solution View → 189

The area of the region ( in square units ) above the x -axis bounded by the curve y = tanx, 0 ≤ x ≤ (π)/(2) and the tangent to the curve at x = (π)/(4) is

JEE Main 2014 Solution View → 190

Let A = \ (x, y): y ^ 2 ≤ 4x, y - 2x ≥ - 4\ . The area of the region A in square units is

JEE Main 2014 Solution View → 191

The area (in sq. unit) of the region described by A = \ (x, y): x ^ 2 + y ^ 2 ≤ 1and y ^ 2 ≤ 1 - x\ is

JEE Main 2014 Solution View → 192

The area enclosed by the curves y = sinx + cosx and y = |cos x - sin x| over the interval [0 , (π)/(2)] is

JEE Advanced 2013 Solution View → 193

Let f:[-2,3] arrow[0, ∞) be a continuous function such that f(1-x)=f(x) for all x ∈[-2,3] . If R_1 is the numerical value of the area of the region bounded by y=f(x), x=-2, x=3

JEE Main 2013 Solution View → 194

The area under the curve y=| x- x| , 0 ≤ x ≤ (π)/(2) , and above x -axis is :

JEE Main 2013 Solution View → 195

The area of the region (in sq. units), in the first quadrant bounded by the parabola y=9 x^2 and the lines x=0, y=1 and y=4 , is :

JEE Main 2013 Solution View → 196

The area bounded by the curve y= (x) and the lines y=0, y= (3) and x=0 is equal to:

JEE Main 2013 Solution View → 197

The area (in square units) bounded by the curves y= x , 2y - x + 3 = 0 , X -axis and lying in the first quadrant is

JEE Main 2013 Solution View → 198

Let S be the area of the region enclosed by y=e^ -x^ 2 , y=0, x=0 and x=1 ; then

JEE Advanced 2012 Solution View → 199

The area bounded by the parabola y^2=4 x and the line 2 x-3 y+4=0 , in square unit, is

JEE Main 2012 Solution View → 200

The area of the region bounded by the curve y=x^3 , and the lines, y=8 , and x=0 , is

JEE Main 2012 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Area Under Curves in other exams

NDA Area Under Curves (54)BITSAT Area Under Curves (24)