Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20207 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
7 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2020 · 7 January · Morning Shift · Mathematics · Area Under Curves

The area of the region (in sq. units), enclosed by the circle x ^ 2...

The area of the region (in sq. units), enclosed by the circle x2+y2=2{x}^{2} + {y}^{2} = 2 which is not common to the region bounded by the parabola y2=x{y}^{2} = x and the straight line y=xy = x, isThe area of the region (in sq. units), enclosed by the circle x ^ 2 + y ^ 2 = 2 which is not common to the region

Options

  1. A16(24π−1)\dfrac{1}{6}\left(24\pi - 1\right)
  2. B13(6π−1)\dfrac{1}{3}\left(6\pi - 1\right)
  3. C13(12π−1)\dfrac{1}{3}\left(12\pi - 1\right)
  4. D16(12π−1)\dfrac{1}{6}\left(12\pi - 1\right)

Correct answer

D. 16(12π−1)\dfrac{1}{6}\left(12\pi - 1\right)

Step-by-step solution

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

Required area

=2π−∫01(x−x)dx= 2\pi - {∫}_{0}^{1}\left(\sqrt{x} - x\right)dx

=2π−(2x323−x22)01= 2\pi - {\left(\dfrac{2x\dfrac{3}{2}}{3} - \dfrac{{x}^{2}}{2}\right)}_{0}^{1}

=2π−(23−12)= 2\pi - \left(\dfrac{2}{3} - \dfrac{1}{2}\right)

=2π−(16)= 2\pi - \left(\dfrac{1}{6}\right)

=12π−16sq.units= \dfrac{12\pi - 1}{6}sq . units

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2… JEE Advanced 2026Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: If… JEE Advanced 2026The area of the region \ (x, y) : x^2 - 8x ≤ y ≤ -x\ is : JEE Main 2026The area of the region \ (x, y) : 0 ≤ y ≤ 6 - x, y^2 ≥ 4x - 3, x ≥ 0\ is: JEE Main 2026The area of the region R = \ (x, y): xy ≤ 27, 1 ≤ y ≤ x^2\ is equal to: JEE Main 2026The area of the region bounded by the curves x+3y^2=0 and x+4y^2=1 is equal to: JEE Main 2026The area of the region \ (x, y): y ≤ π - |x|, y ≤ |x x|, y ≥ 0\ is: JEE Main 2026If the area of the region bounded by 16x^2 - 9y^2 = 144 and 8x - 3y = 24 is A, then 3(A +… JEE Main 2026Let P_ 1 : y=4 x^ 2 and P_ 2 : y=x^ 2 +27 be two parabolas. If the area of the bounded… JEE Main 2026The area of the region R=\ (x, y): x y ≤ 8,1 ≤ y ≤ x^ 2 , x ≥ 0\ is JEE Main 2026Let f(α) denote the area of the region in the first quadrant bounded by x=0, x=1, y^ 2 =x… JEE Main 2026Let A_ 1 be the bounded area enclosed by the curves y=x^ 2 +2, x+y=8 and y -axis that… JEE Main 2026The area of the region enclosed between the circles x^ 2 +y^ 2 =4 and x^ 2 +(y-2)^ 2 =4… JEE Main 2026Let the area of the region bounded by the curve y= \ x, x\ , lines x=0, x=(3 π)/(2) , and… JEE Main 2026The area of the region A=\ (x, y): 4 x^ 2 +y^ 2 8. and .y^ 2 4 x\ is: JEE Main 2026Let the line x=-1 divide the area of the region \ (x, y): 1+x^ 2 ≤ y ≤ 3-x\ in the ratio… JEE Main 2026 Full Area Under Curves list Area Under Curves JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs