Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 2012Offline
Exam
JEE Main
Year
2012
Mode
Offline
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2012 · Offline · Mathematics · Area Under Curves

The area bounded between the parabolas x^2=(y)/(4) and x^2=9 y ,...

The area bounded between the parabolas x2=y4x^2=\frac{y}{4} and x2=9yx^2=9 y, and the straight line y=2y=2 isThe area bounded between the parabolas x^2=(y)/(4) and x^2=9 y , and the straight line y=2 is

Options

  1. A20220 \sqrt{2}
  2. B1023\frac{10 \sqrt{2}}{3}
  3. C2023\frac{20 \sqrt{2}}{3}
  4. D10210 \sqrt{2}

Correct answer

C. 2023\frac{20 \sqrt{2}}{3}

Step-by-step solution

Required area A=2[∫02(3y−y2)dy]=2∫025y2dy=5[y3/23/2]02=103[23/2−0]=2023\begin{aligned} & A=2\left[\int_0^2\left(3 \sqrt{y}-\frac{\sqrt{y}}{2}\right) d y\right]=2 \int_0^2 \frac{5 \sqrt{y}}{2} d y \\ & =5\left[\frac{y^{3 / 2}}{3 / 2}\right]_0^2=\frac{10}{3}\left[2^{3 / 2}-0\right]=\frac{20 \sqrt{2}}{3} \end{aligned} The area bounded between the parabolas x^2=(y)/(4) and x^2=9 y , and the straight line y=2 is
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