2026-05-05 11:50

Status:

Tags:

Proof of the Mean Value Theorem for integrals

Recall: Mean Value Theorem
If the function $\mathbb{f}$ is continuous on the closed interval $\mathbb{[}a,b]$ and differentiable on the open interval $\mathbb{(}a,b)$, there exists a value c on $\mathbb{[}a,b]$ such that:

Then:

Recall: Definition of the area under a curve using Riemann Sums
If a function $\mathbb{f}$ is continuous on the closed interval $\mathbb{[}a,b]$, then the area under the curve wrt to the x-axis is

References