Question

Let f:R→R be a differentiable function such that its derivative f′ is continuous and f(π) = −6. 

If F:[0,π]→R is defined by F(x) = \( \int_0^x \mathrm\,f(t)\,\mathrm{d}t\) , and if, 

\( \int_0^\pi \mathrm\,(f'(x)\,+\,F(x))\,cosx\,\mathrm{d}x\) = 2,

Then the value of (0) is __

Answer 1

Using by part we get