JEE PYQ: Area Under Curves Question 12
Question 12 - 2020 (02 Sep Shift 2)
Consider a region $R = {(x, y) \in \mathbb{R}^2 : x^2 \leq y \leq 2x}$. If a line $y = \alpha$ divides the area of region $R$ into two equal parts, then which of the following is true?
(1) $\alpha^3 - 6\alpha^2 + 16 = 0$
(2) $3\alpha^2 - 8\alpha^{3/2} + 8 = 0$
(3) $3\alpha^2 - 8\alpha + 8 = 0$
(4) $\alpha^3 - 6\alpha^{3/2} - 16 = 0$
Show Answer
Answer: (2) $3\alpha^2 - 8\alpha^{3/2} + 8 = 0$
Solution
Curves intersect at $(0,0)$ and $(2,4)$. Setting equal areas gives $3\alpha^2 - 8\alpha^{3/2} + 8 = 0$.
BETA
