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  •  The area bounded by the curves   and <img alt="\mathrm{ y=

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

Option: 1

\frac{2}{3}(\sqrt{2}+1)


Option: 2

\frac{4}{3}(\sqrt{2}-1)


Option: 3

2(\sqrt{2}-1)


Option: 4

\frac{8}{3}(\sqrt{2}-1)


Answers (1)

best_answer

\mathrm{\text { Area } =2\left[\int_{0}^{1}\left(1-\left(1-x^{2}\right)\right) d x+\int_{1}^{\sqrt{2}}\left(1-\left(x^{2}-1\right) d x\right)\right]}\\

            \mathrm{=2\left[\int_{0}^{1} x^{2} d x+\int_{1}^{\sqrt{2}}\left(2-x^{2}\right) d x\right] }\\

           \mathrm{=2\left[\left.\frac{x^{3}}{3}\right|_{0} ^{1}+\left.2 x\right|_{1} ^{\sqrt{2}}-\left.\frac{x^{3}}{3}\right|_{1} ^{\sqrt{2}}\right]} \\

          =2\left[\frac{1}{3}+2(\sqrt{2}-1)-\frac{1}{3}(2 \sqrt{2}-1)\right] \\

          =\frac{8}{3}(\sqrt{2}-1)

Hence correct option is 4

Posted by

himanshu.meshram

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