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  • The area (in sq.units) of the region enclosed by the curves  and 

The area (in sq.units) of the region enclosed by the curves y=x^{2}-1\; and y=1-x^{2} is equal to :
Option: 1 \frac{4}{3}
 
Option: 2 \frac{8}{3}
Option: 3 \frac{7}{2}  
Option: 4 \frac{16}{3}

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\\\mathrm{A}=\int_{-1}^{1}\left(\left(1-\mathrm{x}^{2}\right)-\left(\mathrm{x}^{2}-1\right)\right) \mathrm{d} \mathrm{x} \\ \\\mathrm{A}=\int_{-1}^{1}\left(\left(2-2 \mathrm{x}^{2}\right) \mathrm{dx}-4 \int_{0}^{1}\left(1-\mathrm{x}^{2}\right) \mathrm{d} \mathrm{x}\right. \\ \\\mathrm{A}=4\left(\mathrm{x}-\frac{\mathrm{x}^{3}}{3}\right)_{0}^{1}=4\left(\frac{2}{3}\right)=\frac{8}{3}

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himanshu.meshram

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