JEE Advanced 2020 Paper 2 Mathematics Q17

Mathematics

Problem

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) = ∫₀ˣ f(t)dt, and if ∫₀^π (f′(x) + F(x)) cos x dx = 2, then the value of f(0) is _____.

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