A) \[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\]
B) \[\left( \frac{\pi }{4}-\sqrt{2}+1 \right)\]
C) \[\left( 1-\frac{\pi }{4}-\sqrt{2} \right)\]
D) \[\left( 1-\frac{\pi }{4}+\sqrt{2} \right)\]
Correct Answer: D
Solution :
\[\int_{\pi /4}^{\beta }{f(x)dx}=\beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \] On differentiating both sides w.r.t.\[\beta \]we get \[f(\beta )=\sin \beta +\beta \cos \beta -\frac{\pi }{4}\sin \beta +\sqrt{2}\] \[\therefore \] \[f\left( \frac{\pi }{2} \right)=1+0-\frac{\pi }{4}+\sqrt{2}\] \[=1-\frac{\pi }{4}+\sqrt{2}\]You need to login to perform this action.
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