A) 1
B) \[\frac{1}{2}\]
C) \[\frac{1}{3}\]
D) None of these
Correct Answer: B
Solution :
[b] We have, \[\int\limits_{0}^{a}{f(x)dx=\frac{{{a}^{2}}}{2}+\frac{a}{2}\sin a+\frac{\pi }{2}\cos a}\] Differentiating w.r.t, we get \[f(a)=a+\frac{1}{2}(\sin a+a\cos a)-\frac{\pi }{2}\sin \,a\] Put \[a=\frac{\pi }{2};f\left( \frac{\pi }{2} \right)=\frac{\pi }{2}+\frac{1}{2}-\frac{\pi }{2}=\frac{1}{2}\]You need to login to perform this action.
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