Question

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

• A. $\frac{2}{3}(\sqrt{2}+1)$
• B. $\frac{4}{3}(\sqrt{2}-1)$
• C. $2(\sqrt{2}-1)$
• D. $\frac{8}{3}(\sqrt{2}-1)$

Answer 1

Answer: (D)

Area $=\text { ABCDEA }$
$ =2\left(\int\limits_0^1\left(1-\left(1-x^2\right)\right) d x+\int\limits_1^{\sqrt{2}}\left(1-\left(x^2-1\right)\right) d x\right)$
$ =\frac{8}{3}(\sqrt{2}-1)$