Let f: {R} \to {R} be a differentiable function such that its derivative f' is continuous and f(\\pi)=-6 . If{F}:[0, \\pi] \to{R} is defined by {F}( {x})=\int_{0}^{ {x}} {f}( {t}) {dt}, and if \int_{0} ^{\\pi} (f'(x)+F(x) ) \cos x d x=2, then the value of f(0) is __________ [JEE Adv 2020 P2]

Definite Integration

Section: Mathematics

Question : 15 of 46

Marks: +1, -0

Let f:R→R be a differentiable function such that its derivative f′ is continuous and f(π)=−6. IfF:[0,π]→R is defined by F(x)=

∫

f(t)dt, and if

∫

(f′(x)+F(x))‌cos‌x‌d‌x=2,
then the value of f(0) is __________

[JEE Adv 2020 P2]

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