# Functions and Calculus-2

Calculus Level 3

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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