A) \[\frac{{{a}^{2}}}{2}\left( \frac{\pi }{2}+1 \right)\]
B) \[\frac{{{a}^{2}}}{2}\left( \frac{\pi }{2}-1 \right)\]
C) \[{{a}^{2}}\left( \frac{\pi }{2}-1 \right)\]
D) None of these
Correct Answer: B
Solution :
[b] Area \[=2\int\limits_{a/\sqrt{2}}^{a}{\sqrt{{{a}^{2}}-{{x}^{2}}}dx}\] \[=2{{\left( \frac{x}{2}\sqrt{{{a}^{2}}-{{x}^{2}}}+\frac{{{a}^{2}}}{2}{{\sin }^{-1}}\frac{x}{a} \right)}^{a}}\] \[=2\left\{ \left( 0+\frac{{{a}^{2}}}{2}.\frac{\pi }{2} \right)-\frac{a}{2\sqrt{2}}-\frac{a}{\sqrt{2}}+\frac{a}{2}.\frac{\pi }{4} \right\}\] \[=\frac{{{a}^{2}}}{2}\left( \frac{\pi }{2}-1 \right)\]You need to login to perform this action.
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