If the area of the region is A, then 3A is equal to __________. [2025]

Question

If the area of the region ${(x, y) : | x - 5 | \leq y \leq 4 \sqrt{x}}$ is A, then 3A is equal to __________. [2025]

Smart Achievers · Accepted Answer

(368)

Area $A = \int_{1}^{25} 4 \sqrt{x} d x - \frac{1}{2} \times 4 \times 4 - \frac{1}{2} \times 20 \times 20$

$= {[4 x^{3 / 2} \times \frac{2}{3}]}_{1}^{25} - 208$

$= \frac{8}{3} (125 - 1) - 208$

$= \frac{368}{3}$ sq. units

$\Rightarrow 3 A = 368$ .

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