Integral Mean Value Theorem

Rarely Tested

Integral Mean Value Theorem

If $$f$$ is continuous and $$g$$ is nonnegative on $$[a,b]$$, then for some $$c\in[a,b]$$:

$$\int_a^bf(x)g(x)\,dx=f(c)\int_a^bg(x)\,dx$$

Usage

- Used when a weighted integral needs to be represented using a single function value.

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