Question

What is the Mean Value Theorem for integrals?

Answer 1

The mean value theorem for integrals:

Statement: If a function $f\left(x\right)$ is continuous on the interval $\left[a,b\right]$, then there exists a point $c\in \left[a,b\right]$ , such that

${\int }_a^{b}f\left(x\right)dx=f\left(c\right)\left(b-a\right)$