QJEEM22Ma4a86: JEE Main 2022 Mathematics - Class 12 JEEM22Ma4a86 Solution: The area of the region enclosed by y ≤ 4 x 2 , x 2 ≤ 9 y and y…

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The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$ , is equal to :

Accepted Answer

JEE Main 2022 (Online) 27th July Evening Shift Mathematics - Area Under The Curves Question 61 English Explanation

$y \leq 4 x^{2}, x^{2} \leq 9 y, y \leq 4$

So, required area

$A = 2 \int_{0}^{4} (3 \sqrt{y} - \frac{1}{2} \sqrt{y}) d y$

$= 2 . \frac{5}{2} {[\frac{2}{3} y^{\frac{3}{2}}]}_{0}^{4}$

$= \frac{10}{3} [4^{\frac{3}{2}} - 0] = \frac{80}{3}$

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