Let f(x) be a non -negative continuous f...

Let f(x) be a non -negative continuous function such that the area bounded by the curve y=f(x), x-axis, and the ordinates `x=pi//4` and `x=betagtpi//4` is `(betasin beta+(pi)/(4)cosbeta+sqrt(2)beta)`. Then `f(pi//2)` is equal to

A

`(pi/4+sqrt(2)-1)`

B

`(pi/4-sqrt(2)+1)`

C

`(1-(pi)/(4)-sqrt(2))`

D

`(1-(pi)/(4)+sqrt(2))`

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The correct Answer is:

D

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