A) \[\left( 1-\frac{\pi }{4}-\sqrt{2} \right)\]
B) \[\left( 1-\frac{\pi }{4}+\sqrt{2} \right)\]
C) \[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\]
D) \[\left( \frac{\pi }{4}-\sqrt{2}+1 \right)\]
Correct Answer: B
Solution :
Given that, \[\int_{\pi /4}^{\beta }{f\ (x)dx}\]\[=\beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \] Differentiating w.r.t. b, we get \[\therefore \] \[f(\beta )=\sin \beta +\beta \cos \beta -\frac{\pi }{4}\sin \beta +\sqrt{2}\], Hence, \[f\ \left( \frac{\pi }{2} \right)=\left( 1-\frac{\pi }{4}+\sqrt{2} \right)\].You need to login to perform this action.
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