A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{8}\]
D) \[0\]
Correct Answer: D
Solution :
Let \[I=\int_{-a}^{a}{x}\sqrt{{{a}^{2}}-{{x}^{2}}}dx\] Again, let \[f(x)=x\sqrt{{{a}^{2}}-{{x}^{2}}}\] \[f(-x)=-x\sqrt{{{a}^{2}}-{{x}^{2}}}\] \[=-f(x)\] \[\therefore \]\[f(x)\]is an odd function. Hence, \[I=0\]
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