JEE MAIN - Mathematics (2025 - 3rd April Evening Shift - No. 1)
The area of the region $\{(x, y):|x-y| \leq y \leq 4 \sqrt{x}\}$ is
$\frac{512}{3}$
$\frac{2048}{3}$
512
$\frac{1024}{3}$
Explanation
$|x-y| \leq y \leq 4 \sqrt{x}$
_3rd_April_Evening_Shift_en_1_1.png)
$$\begin{aligned} & \text { Area }=\int_0^{64}\left(4 \sqrt{x}-\frac{x}{2}\right) d x \\ & \left.=\frac{4 x^{3 / 2}}{\frac{3}{2}}-\frac{x^2}{4}\right]_0^{64} \end{aligned}$$
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