Question 53

Let $$f: R \rightarrow R$$ be a differentiable function such that its derivative $$𝑓′$$ is continuous and $$f(\pi) = -6$$. If $$F:[0, \pi] \rightarrow R$$ is defined by $$F(x) = \int_{0}^{x}f(t)dt $$, and if
$$\int_{0}^{\pi}\left(f'(x) + F(x)\right) \cos x dx = 2 $$, then the value of f(0) is_______

Correct Answer: e

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