If the area of the region {( x , y ) : ∣ x − 5∣ ≤ y ≤ 4 x } is A , then 3 A is equal to _____ .

A = ∫ 1 25 4 x d x − 2 1 × 4 × 4 − 2 1 × 20 × 20 A = [ 2 3 4 x 3/2 ] 25 − 8 − 200 A = 3 8 ( 125 − 1 ) − 208 A = 3 368 ⇒ 3 A = 368

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MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2025

MathematicsMediumnumerical

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

Question diagram: If the area of the region {( x , y ) : ∣ x − 5∣ ≤ y ≤ 4 x

Answer:

368.00

Solution:

$A = \int_{1}^{25} 4 x d x - \frac{1}{2} \times 4 \times 4 - \frac{1}{2} \times 20 \times 20 A = [\frac{4 x ^{3/2}}{\frac{3}{2}}]^{25} - 8 - 200 A = \frac{8}{3} (125 - 1) - 208 A = \frac{368}{3} \Rightarrow 3 A = 368$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2025

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