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.