Let \[f(x)\] be a non-negative continous function such that the area bounded by the curve \[y=f(x)\], x-axis and the ordinates \[x=\frac{\pi }{4}\], \[x=\beta >\frac{\pi }{4}\] is \[\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \right)\]. Then \[f\ \left( \frac{\pi }{2} \right)\] is [AIEEE 2005]

\[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\]

\[\left( 1-\frac{\pi }{4}-\sqrt{2} \right)\]

\[\left( 1-\frac{\pi }{4}+\sqrt{2} \right)\]

\[\left( \frac{\pi }{4}-\sqrt{2}+1 \right)\]

Let \[f(x)\] be a non-negative continous function such that the area b

1.	Let \[f(x)\] be a non-negative continous function such that the area bounded by the curve \[y=f(x)\], x-axis and the ordinates \[x=\frac{\pi }{4}\], \[x=\beta >\frac{\pi }{4}\] is \[\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \right)\]. Then \[f\ \left( \frac{\pi }{2} \right)\] is [AIEEE 2005]
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.	\[\left( \frac{\pi }{4}-\sqrt{2}+1 \right)\]
Answer» C. \[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\]

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