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  4. The area of the region enclosed by y ≤ 4 x 2, x 2 ≤ 9 y and y ≤ 4, is equal to :

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

JEE MainJEE Main 2022Application of Integrals

Solution:

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$\Delta=2 \cdot \int\limits_0^4\left(3 \sqrt{y}-\frac{\sqrt{y}}{2}\right) d y $
$ =2 \cdot \int\limits_0^4 \frac{5}{2} \sqrt{y} d y=\frac{80}{3}$