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JEE Definite Integration PYQs with Solutions

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

692 questionsMathematics2006–2026Answers + solutions

About Definite Integration PYQs

Definite Integration has 692 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (168) and JEE Advanced (52), spanning 2006 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: 31
  • 2025: 23
  • 2024: 37
  • 2023: 39
  • 2022: 42
  • 2021: 8
  • 2020: 2
  • 2019: 2
  • 2018: 2
  • 2017: 3
  • 2016: 1
  • 2015: 7

Definite Integration questions with solutions

1

The value of the definite integral ∫_ 0 ^ 2 1 3^ (x+3)/(2) \, dx is

JEE Advanced 2026 Solution View → 2

The value of the integral ∫_ 0 ^ 2 x(x^2+x+1) ( x+1 )( x^4+x^2+1 ) \, dx is equal to:

JEE Main 2026 Solution View → 3

If ∫_ π/6 ^ π/4 ( (x-(π)/(3)) (x+(π)/(3))+1)dx = α _e( 3 -1) , then 9α^2 is equal to ________.

JEE Main 2026 Solution View → 4

Let A = bmatrix 1 & 3 & -1 2 & 1 & α 0 & 1 & -1 bmatrix be a singular matrix. Let f(x) = ∫ _0^x (t^2 + 2t + 3)\,dt , x ∈ [1, α] . If M and m are respectively the maximum and the

JEE Main 2026 Solution View → 5

Let f: ℝ arrow ℝ be such that f(xy) = f(x)f(y) , for all x, y ∈ ℝ and f(0) ≠ 0 . Let g: [1, ∞) arrow ℝ be a differentiable function such that x^2 g(x) = ∫ _1^x (t^2 f(t)

JEE Main 2026 Solution View → 6

The value of the integral ∫ _ -1 ^ 1 ((x^3 + |x| + 1)/(x^2 + 2|x| + 1)) dx is equal to :

JEE Main 2026 Solution View → 7

The value of the integral ∫_ -π/4 ^ π/4 ( 32 ^4 x 1 + e^ x )dx is:

JEE Main 2026 Solution View → 8

Let (2^ 1-a + 2^ 1+a ) , f(a) , (3^a + 3^ -a ) be in A.P. and α be the minimum value of f(a) . Then the value of the integral ∫_ _e(α-1) ^ _e(α) dx (e^ 2x - e^ -2x ) is :

JEE Main 2026 Solution View → 9

Let f: [1, ∞) arrow R be a differentiable function defined as f(x) = ∫_1^x f(t)\,dt + (1-x)( _e x - 1) + e . Then the value of f(f(1)) is :

JEE Main 2026 Solution View → 10

The value of the integral ∫_0^∞ ( _e(x))/(x^2 + 4)\,dx is:

JEE Main 2026 Solution View → 11

The value of the integral ∫_ π/6 ^ π/3 ((4 - ^2 x)/( ^4 x)) dx is:

JEE Main 2026 Solution View → 12

The integral ∫_ 0 ^ 1 ^ -1 (1+x+x^2)dx is equal to:

JEE Main 2026 Solution View → 13

Let f be a twice differentiable function such that f(x)=∫_ 0 ^ x (t-x)dt-∫_ 0 ^ x f(t) t\,dt , x ∈ (-(π)/(2),(π)/(2)) . Then f''((π)/(6))+12f'(-(π)/(6))+f((π)/(6)) is equal to

JEE Main 2026 Solution View → 14

Let ∫_ -2 ^ 2 (| x| + [x x])\,dx = 2(3 - 2) + β , where [·] is the greatest integer function. Then β ((β)/(2)) equals:

JEE Main 2026 Solution View → 15

The value of ∫_0^ 20π ( ^4 x + ^4 x) \, dx is equal to:

JEE Main 2026 Solution View → 16

Let [·] denote the greatest integer function. Then the value of ∫_0^3 ( e^x + e^ -x [x]! ) dx is :

JEE Main 2026 Solution View → 17

If α = ∫_0^ 2 3 _2(x^2 + 4)\,dx + ∫_2^4 2^x - 4 \,dx , then α^2 is equal to _______.

JEE Main 2026 Solution View → 18

Let [·] denote the greatest integer function. Then ∫_ -(π)/(2) ^ (π)/(2) ((12(3+[x]))/(3+[ x]+[ x])) d x is equal to :

JEE Main 2026 Solution View → 19

Let f be a polynomial function such that f(x^ 2 +1)=x^ 4 +5 x^ 2 +2 , for all x ∈ ℝ . Then ∫_ 0 ^ 3 f(x) d x is equal to

JEE Main 2026 Solution View → 20

If ∫( 1-5 ^ 2 x ^ 5 x ^ 2 x ) d x=f(x)+C , where C is the constant of integration, then f((π)/(6))-f((π)/(4)) is equal to

JEE Main 2026 Solution View → 21

The value of ∑_ r=1 ^ 20 (| π(∫_ 0 ^ r x| π x| d x) |) is \_\_\_\_

JEE Main 2026 Solution View → 22

If f(x) satisfies the relation f(x)=e^ x +∫_ 0 ^ 1 (y+x e^ x ) f(y) d y , then e+f(0) is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 23

Let a differentiable function f satisfy the equation ∫_ 0 ^ 36 f((t x)/(36)) d t=4 α f(x) . If y=f(x) is a standard parabola passing through the points (2,1) and (-4, β) , then β^

JEE Main 2026 Solution View → 24

The number of elements in the set S=\ x: x ∈[0,100]. and .∫_ 0 ^ x t^ 2 (x-t) d t=x^ 2 \ is \_\_\_\_ .

JEE Main 2026 Solution View → 25

The value of the integral ∫_ (π)/(24) ^ (5 π)/(24) ~d x 1+ [3] 2 x is :

JEE Main 2026 Solution View → 26

Let f(x)=[x]^ 2 -[x+3]-3, x ∈ R , where [] is the greatest integer funtion. Then

JEE Main 2026 Solution View → 27

Let [·] be the greatest integer function. If α=∫_ 0 ^ 64 (x^ 1 / 3 -[x^ 1 / 3 ]) d x , then (1)/(π) ∫_ 0 ^ α π ( ^ 2 θ ^ 6 θ+ ^ 6 θ ) d θ is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 28

The value of ∫_ -(π)/(2) ^ (π)/(2) ((1)/([x]+4)) d x , where [·] denotes the greatest integer function, is

JEE Main 2026 Solution View → 29

If ∫_ 0 ^ 1 4 ^ -1 (1-2 x+4 x^ 2 ) d x=atan^ -1 (2)-blog_ e (5) , where a, b ∈ N , then (2 a+b) is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 30

The value of ∫_ -π / 6 ^ π / 6 ( π+4 x^ 11 1- (|x|+π / 6) ) d x is equal to:

JEE Main 2026 Solution View → 31

6 ∫_ 0 ^ π |( 3 x+ 2 x+ x)| d x is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 32

If α=∫_ (1)/(2) ^2 ^ -1 x 2 x^2-3 x+2 d x then the value of 7 ( 2 α 7 π ) is ____________. (Here, the inverse trigonometric function ^ -1 x assumes values in (-(π)/(2), (π)/(2)) .)

JEE Advanced 2025 Solution View → 33

Let f(x) be a positive function and I_1=∫_ -(1)/(2) ^1 2 x f(2 x(1-2 x)) d x and I_2=∫_ -1 ^2 f(x(1-x)) d x . Then the value of (I_2)/(I_1) is equal to ________

JEE Main 2025 Solution View → 34

The integral ∫_ -1 ^ (3)/(2) (|π^2 x (π x)|) d x is equal to:

JEE Main 2025 Solution View → 35

The integral ∫_0^π ((x+3) x)/(1+3 ^2 x) d x is equal to :

JEE Main 2025 Solution View → 36

The value of ∫_ -1 ^1 (1+ |x|-x ) e^x+( |x|-x ) e^ -x e^x+e^ -x d x is equal to

JEE Main 2025 Solution View → 37

The integral ∫_0^π (8 x d x)/(4 ^2 x+ ^2 x) is equal to

JEE Main 2025 Solution View → 38

Let the domain of the function f(x)= _2 _4 _6(3+4 x-x^2) be (a, ~b) . If ∫_0^ b-a [x^2] dx=p- q - r , p, q, r ∈ ℕ, gcd(p, q, r)=1, where [ ·] is the greatest integer function

JEE Main 2025 Solution View → 39

Let (a, b) be the point of intersection of the curve x^2=2 y and the straight line y-2 x-6=0 in the second quadrant. Then the integral I=∫_a^b (9 x^2)/(1+5^x) d x is equal to :

JEE Main 2025 Solution View → 40

4 ∫_0^1( 1 3+x^2 + 1+x^2 ) d x-3 _e( 3 ) is equal to :

JEE Main 2025 Solution View → 41

Let [.] denote the greatest integer function. If ∫_0^ e^3 [ 1 e^ x-1 ] dx=α- _ e 2 , then α^3 is equal to _______ .

JEE Main 2025 Solution View → 42

Let f(x)=∫_0^t t(t^2-9 t+20) d t, 1 ≤ x ≤ 5 . If the range of f is [α, β] , then 4(α+β) equals :

JEE Main 2025 Solution View → 43

If 24 ∫_0^ (π)/(4) ( |4 x-(π)/(12)|+[2 x]) d x=2 π+α , where [·] denotes the greatest integer function, then α is equal to _______.

JEE Main 2025 Solution View → 44

The integral \(80 ∫_0^ (π)/(4) (( θ+ θ)/(9+16 2 θ)) d θ\) is equal to :

JEE Main 2025 Solution View → 45

Let \(f:(0, ∞) arrow R be a twice differentiable function. If for some \( a ≠ 0, ∫_0^1 f(λ x) d λ=a f(x), f(1)=1\) and \(f(16)= (1)/(8) , then \(16-f^ ((1)/(16)) is equal to

JEE Main 2025 Solution View → 46

Let f be a real valued continuous function defined on the positive real axis such that g(x)=∫_0^x t f(t) dt . If g(x^3)=x^6+x^7 , then value of ∑_ r=1 ^ 15 f(r^3) is :

JEE Main 2025 Solution View → 47

Let f: R arrow R be a twice differentiable function such that f(2)=1 . If F(x)=x f(x) for all x ∈ R , ∫_0^2 x ~F^ (x) d x=6 and ∫_0^2 x^2 ~F^ (x) d x=40 , then F^ (2)+∫_0^2 ~F(x)

JEE Main 2025 Solution View → 48

Let for some function y=f(x), ∫_0^x t f(t) d t=x^2 f(x), x 0 and f(2)=3 . Then f(6) is equal to

JEE Main 2025 Solution View → 49

If ∫_ -(π)/(2) ^ (π)/(2) (96 x^2 ^2 x)/((1+e^x)) d x=π(α π^2+β), α, β ∈ ℤ , then (α+β)^2 equals

JEE Main 2025 Solution View → 50

IfI(m, n)=∫_0^1 x^ m-1 (1-x)^ n-1 d x, m, n 0 , then I(9,14)+I(10,13) is

JEE Main 2025 Solution View → 51

If I=∫_0^ (π)/(2) ^ (3)/(2) x ^ (3)/(2) x+ ^ (3)/(2) x ~d x , then ∫_0^ 21 (x x x)/( ^4 x+ ^4 x) ~d x equals :

JEE Main 2025 Solution View → 52

The value of ∫_ e^2 ^ e^4 (1)/(x)( e^ (( _e x)^2+1)^ -1 e^ (( _e x)^2+1)^ -1 +e^ ((6- _e x)^2+1)^ -1 ) d x is

JEE Main 2025 Solution View → 53

Let f(x)=∫_0^ x^2 t^2-8 t+15 e^ t dt, x ∈ R . Then the numbers of local maximum and local minimum points of f , respectively, are :

JEE Main 2025 Solution View → 54

Let for f(x)=7 ^8 x+7 ^6 x-3 ^4 x-3 ^2 x, I_1=∫_0^ π / 4 f(x) d x and I_2=∫_0^ π / 4 x f(x) d x . Then 7 I_1+12 I_2 is equal to :

JEE Main 2025 Solution View → 55

Paragraph: Let \(f: [ 0, (π)/(2)] arrow[ 0,1]\) be the function defined by \(f(x)= ^2 x\) and let \(g: [ 0, (π)/(2)] arrow[ 0, ∞) \) be the function defined by \(g(x)= (π

JEE Advanced 2024 Solution View → 56

Let \(f: [ 0, (π)/(2)] arrow[ 0,1]\) be the function defined by \(f(x)= ^2 x\) and let \(g: [ 0, (π)/(2)] arrow[ 0, ∞) \) be the function defined by \(g(x)= (π x)/(2)-x^2 \). The

JEE Advanced 2024 Solution View → 57

Let ∫_0^x 1-(y^ (t))^2 d t=∫_0^x y(t) d t, 0 ≤ x ≤ 3, y ≥ 0, y(0)=0 . Then at x=2, y^ +y+1 is equal to

JEE Main 2024 Solution View → 58

The value of the integral ∫_ -1 ^2 _e(x+ x^2+1 ) d x is

JEE Main 2024 Solution View → 59

Let ∫_α^ _e 4 d x e^x-1 =(π)/(6) . Then e^α and e^ -α are the roots of the equation :

JEE Main 2024 Solution View → 60

The value of k ∈ N for which the integral I_n=∫_0^1(1-x^k)^n d x, n ∈ ℕ , satisfies 147 I_ 20 =148 I_ 21 is

JEE Main 2024 Solution View → 61

Let [t] denote the largest integer less than or equal to t . If ∫_0^3([x^2]+[(x^2)/(2)]) d x=a+b 2 - 3 - 5 +c 6 - 7 , where a, b, c ∈ Z , then a+b+c is equal to_______

JEE Main 2024 Solution View → 62

∫_0^ π / 4 ( ^2 x ^2 x)/(( ^3 x+ ^3 x)^2) d x is equal to

JEE Main 2024 Solution View → 63

Let r_k= ∫_0^1(1-x^7)^k d x ∫_0^1(1-x^7)^ k+1 d x , k ∈ ℕ . Then the value of ∑_ k=1 ^ 10 (1)/(7(r_k-1)) is equal to________

JEE Main 2024 Solution View → 64

Let β(m, n)=∫_0^1 x^ m-1 (1-x)^ n-1 ~d x, ~m, n>0 . If ∫_0^1(1-x^ 10 )^ 20 ~d x=a × β(b, c) , then 100(a+b+c) equals____

JEE Main 2024 Solution View → 65

If f(t)=∫_0^π 2 x ~d x 1- ^2 t ^2 x , 0 < t < π , then the value of ∫_0^ (π)/(2) π^2 dt f(t) equals_________

JEE Main 2024 Solution View → 66

The value of ∫_ -π ^π (2 y(1+ y))/(1+ ^2 y) d y is :

JEE Main 2024 Solution View → 67

The integral ∫_0^ π / 4 (136 x)/(3 x+5 x) d x is equal to :

JEE Main 2024 Solution View → 68

If the value of the integral ∫_ -1 ^1 ( α x)/(1+3^x) d x is (2)/(π) . Then, a value of α is

JEE Main 2024 Solution View → 69

Let f(x)=\ array lr -2, & -2 ≤ x ≤ 0 x-2, & 0 < x ≤ 2 array . and h(x)=f(|x|)+|f(x)| . Then ∫_ -2 ^2 h(x) d x is equal to :

JEE Main 2024 Solution View → 70

If ∫_0^ (π)/(4) ( ^2 x)/(1+ x x) ~d x= 1 a _ e ( a 3 )+ π b 3 , where a, b ∈ N , then a+b is equal to_________

JEE Main 2024 Solution View → 71

The value of ∫ _ 0 ^ 1 (2 x ^ 3 - 3 x ^ 2 - x + 1)(1)/(3)dx is equal to:

JEE Main 2024 Solution View → 72

If ∫ _ 0 ^ (π)/(3) ^ 4 xdx = aπ + b 3 , where a and b are rational numbers, then 9a + 8b is equal to:

JEE Main 2024 Solution View → 73

Let f: (0, ∞) → R and F(x) = ∫ _ 0 ^ x tf(t)dt . If F( x ^ 2 ) = x ^ 4 + x ^ 5 , then ∑ _ r = 1 ^ 12 f( r ^ 2 ) is equal to:

JEE Main 2024 Solution View → 74

The value of the integral ∫ _ 0 ^ (π)/(4) xdx ^ 4 (2x) + ^ 4 (2x) equals:

JEE Main 2024 Solution View → 75

If ∫ _ - π / 2 ^ π / 2 8 2 cosxdx (1 + e ^ sinx )(1 + ^ 4 x) = απ + β _ e (3 + 2 2 ) , where α, β are integers, then α ^ 2 + β ^ 2 equals __________

JEE Main 2024 Solution View → 76

Let f, g: (0, ∞) → R be two functions defined by f(x) = ∫ _ - x ^ x (|t| - t ^ 2 ) e ^ - t ^ 2 dt and g(x) = ∫ _ 0 ^ x ^ 2 t(1)/(2) e ^ - t ^ 2 dt . Then the value of 9(f( _ e 9 +

JEE Main 2024 Solution View → 77

| 120 π ^ 3 ∫ _ 0 ^ π x ^ 2 sinxcosx ^ 4 x + ^ 4 x dx| is equal to ______.

JEE Main 2024 Solution View → 78

Let f: ℝ → ℝ be a function defined by f(x) = 4 ^ x 4 ^ x + 2 and M = ∫ _ f(a) ^ f(1 - a) x ^ 4 (x(1 - x))dx , N = ∫ _ f(a) ^ f(1 - a) ^ 4 (x(1 - x))dx; a ≠ (1)/(2) . If = , α, β ∈

JEE Main 2024 Solution View → 79

Let S = (- 1, ∞) and f: S → ℝ be defined as f(x) = ∫ _ - 1 ^ x ( e ^ t - 1) ^ 11 (2t - 1) ^ 5 (t - 2) ^ 7 (t - 3) ^ 12 (2t - 10) ^ 61 dt . Let p = Sum of square of the values of x

JEE Main 2024 Solution View → 80

If the integral 525 ∫ _ 0 ^ (π)/(2) sin2xcos(11)/(2)x(1 + cos(5)/(2)x)(1)/(2)dx is equal to (n 2 - 64) , then n is equal to ________

JEE Main 2024 Solution View → 81

Let y = f ( x ) be a thrice differentiable function in ( - 5, 5 ) . Let the tangents to the curve y = f ( x ) at ( 1, f ( 1 ) ) and ( 3, f ( 3 ) ) make angles (π)/(6) and (π)/(4)

JEE Main 2024 Solution View → 82

Let f: R → R be defined f(x) = a e ^ 2x + b e ^ x + cx . If f ( 0 ) = - 1, f ^ ' ( _ e 2) = 21 and ∫ _ 0 ^ log4 (f(x) - cx)dx = (39)/(2) , then the value of | a + b + c | equals:

JEE Main 2024 Solution View → 83

The value 9 ∫ _ 0 ^ 9 [ (10x)/(x + 1) ]dx , where t denotes the greatest integer less than or equal to t , is _____.

JEE Main 2024 Solution View → 84

The value of _ n → ∞ ∑ _ k = 1 ^ n n ^ 3 ( n ^ 2 + k ^ 2 )( n ^ 2 + 3 k ^ 2 ) is :

JEE Main 2024 Solution View → 85

If ∫ _ (π)/(6) ^ (π)/(3) 1 - sin2x dx = α + β 2 + γ 3 , where α, β and γ are rational numbers, then 3α + 4β - γ is equal to _____.

JEE Main 2024 Solution View → 86

If the value of the integral ∫ _ - (π)/(2) ^ (π)/(2) ( x ^ 2 cosx 1 + π ^ x + 1 + ^ 2 x 1 + e ^ (sinx) ^ 2023 )dx = (π)/(4)(π + a) - 2, then the value of a is

JEE Main 2024 Solution View → 87

For x ∈ (- (π)/(2), (π)/(2)) , if y(x) = ∫ cosec x + sinx cosec xsecx + tanx ^ 2 x dx and _ x → ((π)/(2)) ^ - y(x) = 0 then y((π)/(4)) is equal to

JEE Main 2024 Solution View → 88

For 0 < a < 1 , the value of the integral ∫ _ 0 ^ π dx 1 - 2acosx + a ^ 2 is :

JEE Main 2024 Solution View → 89

Let f(x) = ∫ _ 0 ^ x g(t) _ e ((1 - t)/(1 + t))dt , where g is a continuous odd function. If ∫ _ - (π)/(2) ^ (π)/(2) (f(x) + x ^ 2 cosx 1 + e ^ x )dx = ((π)/(α)) ^ 2 - α , then α

JEE Main 2024 Solution View → 90

If ∫ _ 0 ^ 1 1 3 + x + 1 + x dx = a + b 2 + c 3 , where a, b, c are rational numbers, then 2a + 3b - 4c is equal to :

JEE Main 2024 Solution View → 91

If ( a, b ) be the orthocentre of the triangle whose vertices are ( 1, 2 ) , ( 2, 3 ) and ( 3, 1 ) , and I _ 1 = ∫ _ a ^ b xsin(4x - x ^ 2 )dx, I _ 2 = ∫ _ a ^ b sin(4x - x ^ 2

JEE Main 2024 Solution View → 92

For x ∈ ℝ , let ^ - 1 (x) ∈ (- (π)/(2), (π)/(2)) . Then the minimum value of the function f: ℝ → ℝ defined by f(x) = ∫ _ 0 ^ x ^ - 1 x e ^ (t - cost) 1 + t ^ 2023 dt is

JEE Advanced 2023 Solution View → 93

If ∫ _ 0 ^ 1 1 (5 + 2x - 2 x ^ 2 )(1 + e ^ (2 - 4x) ) dx = (1)/(α) _ e ((α + 1)/(β)), α, β > 0 , then α ^ 4 - β ^ 4 is equal to

JEE Main 2023 Solution View → 94

The value of e ^ - (π)/(4) + ∫ _ 0 ^ (π)/(4) e ^ - x tan ^ 50 xdx ∫ _ 0 ^ (π)/(4) e ^ - x ( ^ 49 x + ^ 51 x ) dx

JEE Main 2023 Solution View → 95

Let f _ n = ∫ _ 0 ^ (π)/(2) ( ∑ _ k = 1 ^ n ^ k - 1 x)( ∑ _ k = 1 ^ n ( 2k - 1 ) ^ k - 1 x)cosxdx, n ∈ ℕ . Then f _ 21 - f _ 20 is equal to

JEE Main 2023 Solution View → 96

Among (S1): _ n → ∞ 1 n ^ 2 ( 2 + 4 + 6 + … + 2n ) = 1 (S2): _ n → ∞ 1 n ^ 16 ( 1 ^ 15 + 2 ^ 15 + 3 ^ 15 + … + n ^ 15 ) = (1)/(16)

JEE Main 2023 Solution View → 97

Let for x ∈ ℝ, S _ 0 (x) = x, S _ k (x) = C _ k x + k ∫ _ 0 ^ x S _ k - 1 (t)dt where C _ 0 = 1, C _ k = 1 - ∫ _ 0 ^ 1 S _ k - 1 (x)dx, k = 1, 2, 3, … Then S _ 2 (3) + 6 C _ 3 is

JEE Main 2023 Solution View → 98

If ∫ _ - 0 . 15 ^ 0 . 15 |100 x ^ 2 - 1|dx = (k)/(3000), then k is equal to _____.

JEE Main 2023 Solution View → 99

Let the function f: [0, 2] → ℝ be defined as f(x) = \ cases e ^ min\ x ^ 2 , x - [x]\ , & x ∈ [ 0, 1 ) e ^ [x - _ e x] , & x ∈ [1, 2] cases ), where [t] denotes the greatest

JEE Main 2023 Solution View → 100

If f: ℝ → ℝ be a continuous function satisfying ∫ _ 0 ^ (π)/(2) f(sin2x)sinxdx + α ∫ _ 0 ^ (π)/(4) f(cos2x)cosxdx = 0 , then the value of α is

JEE Main 2023 Solution View → 101

The value of the integral ∫ _ - _ e 2 ^ _ e 2 e ^ x ( _ e ( e ^ x + 1 + e ^ 2x ))dx is equal to

JEE Main 2023 Solution View → 102

For m, n > 0 , let α(m, n) = ∫ _ 0 ^ 2 t ^ m (1 + 3t) ^ n dt . If , 11α(10, 6) + 18α(11, 5) = p (14) ^ 6 , then p is equal to

JEE Main 2023 Solution View → 103

Let f be a continuous function satisfying ∫ _ 0 ^ t ^ 2 (f ( x ) + x ^ 2 )dx = (4)/(3) t ^ 3 , ∀ t > 0 . Then f( π ^ 2 4 ) is equal to

JEE Main 2023 Solution View → 104

Let [ t ] denote the greatest integer function. If ∫ _ 0 ^ 2 . 4 [ x ^ 2 ]dx = α + β 2 + γ 3 + δ 5 , thenα + β + γ + δ is equal to

JEE Main 2023 Solution View → 105

Let [ t ] denote the greatest integer ≤ t . Then (2)/(π) ∫ _ (π)/(6) ^ (5π)/(6) (8[cosecx] - 5[cotx])dx is equal to _______

JEE Main 2023 Solution View → 106

Let f(x) be a function satisfying f(x) + f(π - x) = π ^ 2 , ∀ x ∈ ℝ . Then ∫ _ 0 ^ π f(x)sinxdx is equal to

JEE Main 2023 Solution View → 107

Let f(x) = x (1 + x ^ n ) ^ (1)/(n) , x ∈ ℝ - \ - 1\ , n ∈ ℕ, n > 2 . If f ^ n (x) = ( fofof . . . . upto n times) (x) , then _ n → ∞ ∫ _ 0 ^ 1 x ^ n - 2 ( f ^ n (x))dx is equal to

JEE Main 2023 Solution View → 108

The value of the integral ∫ _ - (π)/(4) ^ (π)/(4) (x + (π)/(4))/(2 - cos2x)dx is :

JEE Main 2023 Solution View → 109

If ∫ _ 0 ^ π 5 ^ cosx (1 + cosxcos3x + ^ 2 x + ^ 3 xcos3x)dx 1 + 5 ^ cosx = (kπ)/(16) , then k is equal to _____ .

JEE Main 2023 Solution View → 110

_ n → ∞ ((1)/(1 + n) + (1)/(2 + n) + (1)/(3 + n) + … + (1)/(2n)) is equal to :-

JEE Main 2023 Solution View → 111

If ∫ _ 0 ^ 1 ( x ^ 21 + x ^ 14 + x ^ 7 ) (2 x ^ 14 + 3 x ^ 7 + 6) ^ 1 / 7 dx = (1)/(l) (11) ^ m / n where l, m, n ∈ N, m and n are co-prime then l + m + n is equal to _____ .

JEE Main 2023 Solution View → 112

Let α > 0 . If ∫ _ 0 ^ α x x + α - x dx = 16 + 20 2 15 then α is equal to :

JEE Main 2023 Solution View → 113

If ϕ ( x ) = 1 x ∫ _ (π)/(4) ^ x (4 2 sint - 3 ϕ ^ ' ( t ))dt, x > 0 then ϕ ^ ' ((π)/(4)) is equal to

JEE Main 2023 Solution View → 114

Let α ∈ (0, 1) and β = _ e (1 - α) . Let P _ n (x) = x + x ^ 2 2 + x ^ 3 3 + … . + x ^ n n , x ∈ (0, 1) . Then the integral ∫ _ 0 ^ α t ^ 50 1 - t dt is equal to

JEE Main 2023 Solution View → 115

The value of ∫ _ (π)/(3) ^ (π)/(2) ((2 + 3sinx))/(sinx(1 + cosx))dx is equal to

JEE Main 2023 Solution View → 116

Let a differentiable function f satisfy f(x) + ∫ _ 3 ^ x (f(t))/(t)dt = x + 1 , x ≥ 3 . Then 12f(8) is equal to:

JEE Main 2023 Solution View → 117

_ n → ∞ (3)/(n)\ 4 + (2 + (1)/(n)) ^ 2 + (2 + (2)/(n)) ^ 2 + … + (3 - (1)/(n)) ^ 2 \ is equal to

JEE Main 2023 Solution View → 118

If [ t denotes the greatest integer ≤ 1 , then the value of (3(e - 1))/(e) ∫ _ 1 ^ 2 x ^ 2 e ^ [x] + [ x ^ 3 ] dx is :

JEE Main 2023 Solution View → 119

_ x → 0 48 x ^ 4 ∫ _ 0 ^ x t ^ 3 t ^ 6 + 1 dt is equal to

JEE Main 2023 Solution View → 120

The value of the integral ∫ _ 1 ^ 2 ( t ^ 4 + 1 t ^ 6 + 1 )dt is :

JEE Main 2023 Solution View → 121

The value of the integral ∫ _ 1 / 2 ^ 2 ^ - 1 x x dx is equal to

JEE Main 2023 Solution View → 122

Let f(x) = x + a π ^ 2 - 4 sinx + b π ^ 2 - 4 cosx , x ∈ ℝ be a function which satisfies f(x) = x + ∫ _ 0 ^ π / 2 sin(x + y)f(y)dy . Then (a + b) is equal to

JEE Main 2023 Solution View → 123

Let [x] denote the greatest integer ≤ x . Consider the function f ( x ) = max\ x ^ 2 , 1 + [ x ]\ . Then the value of the integral ∫ _ 0 ^ 2 f ( x ) dx is :

JEE Main 2023 Solution View → 124

The integral 16 ∫ _ 1 ^ 2 dx x ^ 3 ( x ^ 2 + 2) ^ 2 is equal to

JEE Main 2023 Solution View → 125

If ∫ _ (1)/(3) ^ 3 | _ e x|dx = (m)/(n) _ e ( n ^ 2 e ) , where m and n are coprime natural numbers, then m ^ 2 + n ^ 2 - 5 is equal to _____ .

JEE Main 2023 Solution View → 126

The minimum value of the function f(x) = ∫ _ 0 ^ 2 e ^ |x - t| dt is

JEE Main 2023 Solution View → 127

∫ _ 3 2 4 ^ 3 3 4 48 9 - 4 x ^ 2 dx is equal to

JEE Main 2023 Solution View → 128

Let f be a differentiable function defined on [0, (π)/(2)] such that f(x) > 0 and f(x) + ∫ _ 0 ^ x f(t) 1 - ( _ e (f(t))) ^ 2 dt = e ∀ x ∈ [0, (π)/(2)] , then \ 6 _ e

JEE Main 2023 Solution View → 129

The value of (8)/(π) ∫ _ 0 ^ (π)/(2) (cosx) ^ 2023 (sinx) ^ 2023 + (cosx) ^ 2023 dx is ______.

JEE Main 2023 Solution View → 130

The value of 12 ∫ _ 0 ^ 3 | x ^ 2 - 3x + 2|dx is ______

JEE Main 2023 Solution View → 131

The greatest integer less than or equal to ∫ _ 1 ^ 2 _ 2 ( x ^ 3 + 1)dx + ∫ _ 1 ^ _ 2 9 ( 2 ^ x - 1)(1)/(3)dx is

JEE Advanced 2022 Solution View → 132

For positive integer n , define f(n) = n + 16 + 5n - 3 n ^ 2 4n + 3 n ^ 2 + 32 + n - 3 n ^ 2 8n + 3 n ^ 2 + 48 - 3n - 3 n ^ 2 12n + 3 n ^ 2 + … + 25n - 7 n ^ 2 7 n ^ 2 . Then, the

JEE Advanced 2022 Solution View → 133

Consider the equation ∫ _ 1 ^ e ( _ e x) ^ (1)/(2) x (a - ( _ e x) ^ (3)/(2) ) ^ 2 dx = 1, a ∈ (- ∞ , 0) ∪ (1, ∞) . Which of the following statements is/are TRUE?

JEE Advanced 2022 Solution View → 134

If [t] denotes the greatest integer ≤ t , then the value of ∫ _ 0 ^ 1 [2x - |3 x ^ 2 - 5x + 2| + 1]dx is

JEE Main 2022 Solution View → 135

The integral ∫ _ 0 ^ (π)/(2) (1)/(3 + 2sinx + cosx)dx is equal to:

JEE Main 2022 Solution View → 136

If f(α) = ∫ _ 1 ^ α _ 10 t 1 + t dt, α > 0 , then f( e ^ 3 ) + f( e ^ - 3 ) is equal to

JEE Main 2022 Solution View → 137

Let I _ n (x) = ∫ _ 0 ^ x 1 ( t ^ 2 + 5) ^ n dt, n = 1, 2, 3, … . Then

JEE Main 2022 Solution View → 138

The value of the integral ∫ _ 0 ^ (π)/(2) 60(sin(6x))/(sinx)dx is equal to

JEE Main 2022 Solution View → 139

The minimum value of the twice differentiable function f(x) = ∫ _ 0 ^ x e ^ x - t f ^ ' (t)dt - ( x ^ 2 - x + 1) e ^ x , x ∈ R , is

JEE Main 2022 Solution View → 140

If ∫ _ 0 ^ 3 15 x ^ 3 1 + x ^ 2 + (1 + x ^ 2 ) ^ 3 dx = α 2 + β 3 , where α, β are integers, then α + β is equal to

JEE Main 2022 Solution View → 141

∫ _ 0 ^ 2 (|2 x ^ 2 - 3x| + [x - (1)/(2)])dx , where [t] is the greatest integer function, is equal to

JEE Main 2022 Solution View → 142

Let f(x) = min\ [x - 1], [x - 2], … , [x - 10]\ where [t] denotes the greatest integer ≤ t . Then ∫ _ 0 ^ 10 f(x)dx + ∫ _ 0 ^ 10 (f(x)) ^ 2 dx + ∫ _ 0 ^ 10 |f(x)|dx is equal

JEE Main 2022 Solution View → 143

Let f be a differentiable function satisfying f(x) = 2 3 ∫ _ 0 ^ 3 f( λ ^ 2 x 3 )dλ, x > 0 and f(1) = 3 . If y = f(x) passes through the point (α, 6) , then α is equal to _______.

JEE Main 2022 Solution View → 144

I = ∫ _ (π)/(4) ^ (π)/(3) ((8sinx - sin2x)/(x))dx . Then

JEE Main 2022 Solution View → 145

∫ _ 0 ^ 20π (|sinx| + |cosx|) ^ 2 dx is equal to:

JEE Main 2022 Solution View → 146

If a = _ n → ∞ ∑ _ k = 1 ^ n 2n n ^ 2 + k ^ 2 and f(x) = (1 - cosx)/(1 + cosx) , x ∈ (0, 1) , then:

JEE Main 2022 Solution View → 147

If n(2n + 1) ∫ _ 0 ^ 1 (1 - x ^ n ) ^ 2n dx = 1177 ∫ _ 0 ^ 1 (1 - x ^ n ) ^ 2n + 1 dx , then n ∈ N is equal to _______.

JEE Main 2022 Solution View → 148

_ n → ∞ 1 2 ^ n ( 1 1 - 1 2 ^ n + 1 1 - 2 2 ^ n + 1 1 - 3 2 ^ n + … . + 1 1 - 2 ^ n - 1 2 ^ n ) is equal to

JEE Main 2022 Solution View → 149

Let [t] denote the greatest integer less than or equal to t . Then the value of the integral ∫ _ - 3 ^ 101 ([sin( )] + e ^ [cos(2 )] )dx is equal to

JEE Main 2022 Solution View → 150

Let f be a twice differentiable function on R . If f ^ ' (0) = 4 and f(x) + ∫ _ 0 ^ x (x - t) f ^ ' (t)dt = ( e ^ 2x + e ^ - 2x )cos2x + (2)/(a)x , then (2a + 1) ^ 5 a ^ 2 is

JEE Main 2022 Solution View → 151

Let a _ n = ∫ _ - 1 ^ n (1 + (x)/(2) + x ^ 2 3 + … + x ^ n - 1 n )dx for every n ∈ N . Then the sum of all the elements of the set \ n ∈ N: a _ n ∈ (2, 30)\ is _________.

JEE Main 2022 Solution View → 152

For any real number x , let [x] denote the largest integer less than or equal to x . Let f be a real-valued function defined on the interval [- 10, 10] by f(x) = \ cases x - [x]

JEE Main 2022 Solution View → 153

If _ n → ∞ (n + 1) ^ k - 1 n ^ k + 1 [( nk + 1 ) + ( nk + 2 ) + … + (nk + n)] = 33 . _ n → ∞ 1 n ^ k + 1 · [ 1 ^ k + 2 ^ k + 3 ^ k + … + n ^ k ] , then the integral value of k is

JEE Main 2022 Solution View → 154

Let f be a real valued continuous function on [0, 1] and f(x) = x + ∫ _ 0 ^ 1 (x - t)f(t)dt . Then which of the following points (x, y) lies on the curve y = f (x)?

JEE Main 2022 Solution View → 155

If ∫ _ 0 ^ 2 ( 2x - 2x - x ^ 2 )dx = ∫ _ 0 ^ 1 (1 - 1 - y ^ 2 - y ^ 2 2 )dy + ∫ _ 1 ^ 2 (2 - y ^ 2 2 )dy + I , then I equal to

JEE Main 2022 Solution View → 156

∫ _ 0 ^ 5 cos(π(x - [(x)/(2)]))dx , where [t] denotes greatest integer less than or equal to t , is equal to

JEE Main 2022 Solution View → 157

Let f: R → R be a differentiable function such that f((π)/(4)) = 2 , f((π)/(2)) = 0 and f ^ ' ((π)/(2)) = 1 and let g(x) = ∫ _ x ^ (π)/(4) ( f ^ ' (t)sect + tantsectf(t))dt for x

JEE Main 2022 Solution View → 158

Let f: R → R be continuous function satisfying f(x) + f(x + k) = n , for all x ∈ R where k > 0 and n is a positive integer. If I _ 1 = ∫ _ 0 ^ 4nk f(x)dx and I _ 2 = ∫ _ - k ^ 3k

JEE Main 2022 Solution View → 159

Let [t] denote the greatest integer less than or equal to t . Then, the value of the integral ∫ _ 0 ^ 1 [- 8 x ^ 2 + 6x - 1]dx is equal to

JEE Main 2022 Solution View → 160

Let f be a differentiable function in (0, (π)/(2)) . If ∫ _ cosx ^ 1 t ^ 2 f(t)dt = ^ 3 x + cosx , then 1 3 f ^ ' ( 1 3 ) is equal to

JEE Main 2022 Solution View → 161

The integral ∫ _ 0 ^ 1 1 7 ^ [(1)/(x)] dx , where [·] denotes the greatest integer function, is equal to

JEE Main 2022 Solution View → 162

The value of the integral ∫ _ - 2 ^ 2 | x ^ 3 + x| ( e ^ x|x| + 1) dx is equal to

JEE Main 2022 Solution View → 163

The integral (24)/(π) ∫ _ 0 ^ 2 (2 - x ^ 2 )dx (2 + x ^ 2 ) 4 + x ^ 4 is equal to ______.

JEE Main 2022 Solution View → 164

Let f(x) = max\ |x + 1|, |x + 2|, … , |x + 5|\ . Then ∫ _ - 6 ^ 0 f(x)dx is equal to ______.

JEE Main 2022 Solution View → 165

The value of the integral 48 π ^ 4 ∫ _ 0 ^ π ( 3π x ^ 2 2 - x ^ 3 ) sinx 1 + ^ 2 x dx is equal to ______.

JEE Main 2022 Solution View → 166

If b _ n = ∫ _ 0 ^ (π)/(2) ^ 2 nx sinx dx, n ∈ ℕ , then

JEE Main 2022 Solution View → 167

The value of b > 3 for which 12 ∫ _ 3 ^ b 1 ( x ^ 2 - 1)( x ^ 2 - 4) dx = _ e ((49)/(40)) , is equal to _____.

JEE Main 2022 Solution View → 168

The value of ∫ _ 0 ^ π e ^ cosx sinx (1 + ^ 2 x)( e ^ cosx + e ^ - cosx ) dx is equal to

JEE Main 2022 Solution View → 169

The value of the integral ∫ _ - (π)/(2) ^ (π)/(2) dx (1 + e ^ x )( ^ 6 x + ^ 6 x) is equal to

JEE Main 2022 Solution View → 170

_ n → ∞ ( n ^ 2 ( n ^ 2 + 1)(n + 1) + n ^ 2 ( n ^ 2 + 4)(n + 2) + n ^ 2 ( n ^ 2 + 9)(n + 3) + … + n ^ 2 ( n ^ 2 + n ^ 2 )(n + n) ) is equal to

JEE Main 2022 Solution View → 171

If f(θ) = sinθ + ∫ _ - (π)/(2) ^ (π)/(2) (sinθ + tcosθ) · f(t)dt , then | ∫ _ 0 ^ (π)/(2) f(θ)dθ| is

JEE Main 2022 Solution View → 172

Let Max _ 0 ⩽ x ⩽ 2 \ 9 - x ^ 2 5 - x \ = α and Min _ 0 ⩽ x ⩽ 2 \ 9 - x ^ 2 5 - x \ = β . If ∫ _ β - (8)/(3) ^ 2α - 1 Max \ 9 - x ^ 2 5 - x , x\ dx = α _ 1 + α _ 2 _ e ((8)/(15))

JEE Main 2022 Solution View → 173

Let f: [- (π)/(2), (π)/(2)] → ℝ be a continuous function such that f(0) = 1 and ∫ _ 0 ^ (π)/(3) f(t)dt = 0 Then which of the following statements is (are) TRUE?

JEE Advanced 2021 Solution View → 174

Let g_ i :[(π)/(8), (3 π)/(8)] arrow ℝ, i=1,2 , and f:[(π)/(8), (3 π)/(8)] arrow ℝ be functions such that g_ 1 (x)=1, g_ 2 (x)=|4 x-π| and f(x)= ^ 2 x , for all x ∈[(π)/(8), (3

JEE Advanced 2021 Solution View → 175

Let g_ i :[(π)/(8), (3 π)/(8)] arrow ℝ, i=1,2 , and f:[(π)/(8), (3 π)/(8)] arrow ℝ be functions such that g_ 1 (x)=1, g_ 2 (x)=|4 x-π| and f(x)= ^ 2 x , for all x ∈[(π)/(8), (3

JEE Advanced 2021 Solution View → 176

For any real number x , let [x] denotes the largest integer less than or equal to x . If I = ∫ _ 0 ^ 10 [ (10x)/(x + 1) ]dx , then the value of 9I is ____.

JEE Advanced 2021 Solution View → 177

Let f: R → R be a continuous function. Then _ x → π / 4 (π)/(4) ∫ _ 2 ^ sec ^ 2 x f ( x ) dx x ^ 2 - π ^ 2 16 is equal to:

JEE Main 2021 Solution View → 178

Let J _ n, m = ∫ _ 0 ^ 1 / 2 x ^ n x ^ m - 1 dx, ∀ n > m and n, m ∈ N . Consider a matrix A = [ a _ ij ] _ 3 × 3 where a _ ij = \ cases J _ 6 + i, 3 - J _ i + 3, 3 & , i ≤ j 0 &

JEE Main 2021 Solution View → 179

The function f ( x ) , that satisfies the condition f ( x ) = x + ∫ _ 0 ^ π / 2 sinxcosyf ( y ) dy, is :

JEE Main 2021 Solution View → 180

If [x] is the greatest integer ≤ x, then π ^ 2 ∫ _ 0 ^ 2 (sin( )/(2)) (x - [x]) ^ [ x ] dx is equal to :

JEE Main 2021 Solution View → 181

Let f: ℝ → ℝ be a differentiable function such that its derivative f ^ ' is continuous and f(π) = - 6 . If F: [0, π] → ℝ is defined by F(x) = ∫ _ 0 ^ x f(t)dt, and if ∫ _ 0 ^ π (

JEE Advanced 2020 Solution View → 182

Which of the following inequalities is/are TRUE?

JEE Advanced 2020 Solution View → 183

The value of the integral ∫ _ 0 ^ π / 2 3 cos ⁡ θ ( cos ⁡ θ + sin ⁡ θ ) ^ 5 dθ equals

JEE Advanced 2019 Solution View → 184

If I = (2)/(π) ∫ _ - (π)/(4) ^ (π)/(4) dx (1 + e ^ sinx )(2 - cos2x) then find 27 I ^ 2 equals____

JEE Advanced 2019 Solution View → 185

The value of the integral ∫ _ 0 ^ (1)/(2) 1 + 3 ( (x + 1) ^ 2 (1 - x) ^ 6 )(1)/(4) dx is

JEE Advanced 2018 Solution View → 186

Let f: ℝ → ℝandg: ℝ → ℝ be two non-constant differentiable functions. If f ^ ′ (x) = ( e ^ (f(x)) - g(x) ) g ^ ′ (x)forallx ∈ ℝ , and f(1) = g(2) = 1 then which of the following

JEE Advanced 2018 Solution View → 187

The value of I = ∑ _ k = 1 ^ 98 ∫ _ k ^ k + 1 (k + 1)/(x ( x + 1 )) dx, then

JEE Advanced 2017 Solution View → 188

If g(x) = ∫ _ sinx ^ sin2x ^ - 1 tdt, then

JEE Advanced 2017 Solution View → 189

Let f: ℝ → ℝ be a differentiable function such that f(0) = 0, f((π)/(2)) = 3 and f ^ ′ (0) = 1 . If g(x) = ∫ _ x ^ (π)/(2) [ f ^ ′ (t)cosect - cottcosectf(t)]dt , for x ∈ (0

JEE Advanced 2017 Solution View → 190

The value of ∫ _ - (π)/(2) ^ (π)/(2) x ^ 2 cos ⁡ x 1 + e ^ x dx is equal to

JEE Advanced 2016 Solution View → 191

If α = ∫ _ 0 ^ 1 ( e ^ 9x + 3 ^ - 1 ⁡ x )( 12 + 9 x ^ 2 1 + x ^ 2 )dx where ^ - 1 ⁡ x takes only principal values, then the value of ( _ e ⁡ |1 + α| - (3π)/(4)) is

JEE Advanced 2015 Solution View → 192

The option(s) with the value of a and L that satisfy the following equation is(are) ∫ _ 0 ^ 4π e ^ t ( ^ 6 ⁡ at + ^ 4 ⁡ at)dt ∫ _ 0 ^ π ( ^ 6 ⁡ at + ^ 4 ⁡ at)dt = L ?

JEE Advanced 2015 Solution View → 193

Let f(x) = 7 ^ 8 ⁡ x + 7 ^ 6 ⁡ x - 3 ^ 4 ⁡ x - 3 ^ 2 ⁡ x for all x ∈ (- (π)/(2), (π)/(2)) . Then the correct expression(S) is(are)

JEE Advanced 2015 Solution View → 194

Let f ^ ′ (x) = 192 x ^ 3 2 + ^ 4 ⁡ for all x ∈ ℝ with f((1)/(2)) = 0 . If m ≤ ∫ _ (1)/(2) ^ 1 f(x)dx ≤ M, then the possible values of m and M are

JEE Advanced 2015 Solution View → 195

Let F: ℝ → ℝ be a thrice differentiable function. Suppose that F(1) = 0, F(3) = - 4 and F′(x) If ∫ _ 1 ^ 3 x ^ 2 F ^ ′ (x)dx = - 12 and ∫ _ 1 ^ 3 x ^ 3 F ^ ′′ (x)dx = 40, then the

JEE Advanced 2015 Solution View → 196

Let f: ℝ → ℝ be a function defined by f(x) = \ cases [x], & x ≤ 2 0, & x > 2 cases ) , where [ x ] is the greatest integer less than or equal to x . If I = ∫ _ - 1 ^ 2 xf ( x ^ 2

JEE Advanced 2015 Solution View → 197

Let F(x) = ∫ _ x ^ x ^ 2 + (π)/(6) 2 ^ 2 ⁡ tdt for all x ∈ ℝand f: [0, (1)/(2)] → [0, ∞) be a continuous function. For a ∈ [0, (1)/(2)], if F ^ ′ (a) + 2 is the area of the region

JEE Advanced 2015 Solution View → 198

The following integral ∫ _ (π)/(4) ^ (π)/(2) (2cosecx) ^ 17 dx is equal to

JEE Advanced 2014 Solution View → 199

Paragraph: Given that for each a ∈(0,1) , _ h arrow 0^ + ∫_ h ^ 1-h t^ -a (1-t)^ a-1 d t exists. Let this limit be g(a) . In addition, it is given that the function g(a) is

JEE Advanced 2014 Solution View → 200

Paragraph: Given that for each a ∈(0,1) , _ h arrow 0^ + ∫_ h ^ 1-h t^ -a (1-t)^ a-1 d t exists. Let this limit be g(a) . In addition, it is given that the function g(a) is

JEE Advanced 2014 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)Determinants (508)

Definite Integration in other exams

NDA Definite Integration (110)BITSAT Definite Integration (22)