JEE Main 2025 Apr 4 Shift 1, Mathematics Q21: Area as Definite Integral

JEE Main2025Apr 4, Shift 1Mathematics

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

Your answer

Solution

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

$= [\frac{8}{3} x^{3/2}]_{1}^{25} - 8 - 200$

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

$= \frac{992}{3} - 208$

$= \frac{368}{3}$

$∴ 3 A = 368$

Concept behind this question

Concept-wise practice with instant solutions on Fundamenthol.