Let f(x) be a non negative continuous function such that area bounded by the curve y = f(x), the x-axis and the ordinates x=π4 and x=β>π4 is βsinβ+π4cosβ+2β . Then f(π2) =

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π4−2+1

π4+2−1

1−π4+2

1+π4+2

answer is C.

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Detailed Solution

∫π4βf(x)dx=βsinβ+π4cosβ+2 β Ditterentiating w.r.t β ,f(β)=sinβ+βcosβ−π4sinβ+2f(π2)=1−π4+2

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