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

Question

Aicharya · Accepted Answer

$\begin{aligned} & A=\int_1^{25} 4 \sqrt{x} d x-\frac{1}{2} \times 4 \times 4-\frac{1}{2} \times 20 \times 20 \\ & A=\left[\frac{4 x^{3 / 2}}{\frac{3}{2}}\right]^{25}-8-200 \\ & A=\frac{8}{3}(125-1)-208 \\ & A=\frac{368}{3} \Rightarrow 3 A=368\end{aligned}$

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

Solution