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JEE Main 20254 AprilMorning Shift

Exam: JEE Main
Year: 2025
Date: 4 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2025 · 4 April · Morning Shift · Mathematics · Area Under Curves

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

If the area of the region

\{(x, y):|x-5| \leq y \leq 4 \sqrt{x}\}

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

Correct answer

0

Step-by-step solution

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

\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}

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