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JEE Main 202524 JanuaryMorning Shift

Exam: JEE Main
Year: 2025
Date: 24 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2025 · 24 January · Morning Shift · Mathematics · Area Under Curves

The area of the region \ (x, y): x^2+4 x+2 ≤ y ≤|x+2|\ is equal to

The area of the region

\left\{(x, y): x^2+4 x+2 \leq y \leq|x+2|\right\}

is equal to $The area of the region \ (x, y): x^2+4 x+2 ≤ y ≤|x+2|\ is equal to$

Options

A $7$
B $5$
C $24 / 5$
D $20 / 3$

Correct answer

D. $20 / 3$

Step-by-step solution

x^2+4 x+2 \leq y \leq|x+2|

$The area of the region \ (x, y): x^2+4 x+2 ≤ y ≤|x+2|\ is equal to$

\begin{aligned} & A_1=\int_{-4}^0\left[2-\left(x^2+4 x+2\right)\right] d x-\frac{1}{2} \times 4 \times 2 \\ & =\left(\frac{-x^3}{3}-2 x^2\right)_{-4}^0-4 \\ & =0-\left(\frac{64}{3}-32\right)-4 \\ & =32-\frac{64}{3}-4=\frac{20}{3}\end{aligned}

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