JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q20

MathematicsSingle correct+4 / -1Question 20 of 90

The area bounded by the curves $y=\left|x^2-1\right|$ and $y=1$ is

\dfrac23\left(\sqrt2+1\right)

\dfrac43\left(\sqrt2-1\right)

2\left(\sqrt2-1\right)

\dfrac83\left(\sqrt2-1\right)

Answer and worked solution

Official answer: D

Intersections at $x=0,\pm\sqrt2$ .

Area $=2\left[\int_0^1x^2dx+\int_1^{\sqrt2}(2-x^2)dx\right]=2\left[\frac13+\frac{4\sqrt2}3-\frac53\right]=\frac83\left(\sqrt2-1\right)$ .

(D)

Topics:Area between curves

JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 20