Functions and Calculus-2

Calculus Level 4

Let \(f(x) \) be a function satisfying \(f'(x) = f(x) \) with \(f(0) = 1\) and \(g\) be a function satisfying \(f(x) + g(x) = x\). Compute \( \displaystyle \int_0^1 f(x) g(x) \, dx \).

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