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

Correct answer: 368. A=∫_1^25 4 √x d x-1/2 × 4 × 4-1/2 × 20 × 20 A= [frac4 x^3 / 23/2 ]^25-8-200 A=8/3(125-1)-208 A=368/3 ⇒ 3 A=368

Q26 / 75 · JEE Main 2025 (4 Apr Shift 1) · Mathematics

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

Correct answer: 368

Solution

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

Hence, the correct answer is 368.

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

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