Fubini 's Theorem

In Mathematical analysis, the Fubini's theorem is sometimes useful. Below is a weak form of Fubini 's Theorem.

What is Fubini 's Theorem?

If

is continuous, then the repeated integrals below

 and

exist and are equal. We shall often find the need to differentiate an integral with varying limits of integration. This weak version or form of Fubini's Theorem should be memorized. There are many other math analysis results that are based on Fubini 's Theorem result and we shall prove them in another section. Fubini 's Theorem extends from the Fundamental Theorem of Calculus below.

Fundamental Theorem of Calculus

If the function below is continuously differentiable:

Then: