If the area of the region \ (x, y): x-5 leq y leq 4 √(x)\ is A , then 3 A is equal to

Mathematics · Area under the Curves

JEE Main 2025 — 4 April, Morning Shift — Question 41

If the area of the region $\{(x, y):|x-5| \leq y \leq 4 \sqrt{x}\}$ is $A$ , then $3 A$ is equal to $\qquad$

Numerical answer — enter this value.

Area $=\int_{1}^{25} 4 \sqrt{x} d x-\frac{1}{2} \times(5-1) \cdot 4-\frac{1}{2} \times(25-5) \times 20$

$=4\left[\frac{2}{3} x^{\frac{3}{2}}\right]_{1}^{25}-8-200=\frac{368}{3}$

$\Rightarrow 3 A=368$

Answer key and solution verified before publishing.

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