JEE Main 2022 · 24 Jun · Shift 2 · Mathematics Q26

MathematicsInteger+4 / -1Question 26 of 90

The area (in sq. units) of the region enclosed between the parabola $y^2=2x$ and the line $x+y=4$ is ______.

Your answer

Answer and worked solution

Official answer: 18

Intersections. $\frac{y^2}2=4-y$ gives $y^2+2y-8=0$ , $y=2$ or $-4$ .

Area (integrate in $y$ ):
$\int_{-4}^2\left(4-y-\frac{y^2}2\right)dy=\left[4y-\frac{y^2}2-\frac{y^3}6\right]_{-4}^2=\frac{14}3+\frac{40}3=18.$

Answer: 18

JEE Main 2022 · 24 Jun · Shift 2, Mathematics question 26