JEE MAIN - Mathematics (2025 - 4th April Morning Shift - No. 24)
If the area of the region $\{(x, y):|x-5| \leq y \leq 4 \sqrt{x}\}$ is $A$, then $3 A$ is equal to _________.
Answer
368
Explanation
$$\begin{aligned} & \text { Area }=\int_1^{25} 4 \sqrt{x} d x-\frac{1}{2} \times(5-1) \cdot 4-\frac{1}{2} \times(25-5) \times 20 \\ & =4\left[\frac{2}{3} x^{\frac{3}{2}}\right]_1^{25}-8-200=\frac{368}{3} \\ & \Rightarrow 3 A=368 \end{aligned}$$
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