## The Fundamental Theorem of Calculus

Read this section to see the connection between derivatives and integrals. Work through practice problems 1-5.

### Leibniz' Rule For Differentiating Integrals

If the endpoint of an integral is a function of rather than simply , then we need to use the Chain Rule together with part 1 of the Fundamental Theorem of Calculus to calculate the derivative of the integral. According to the Chain Rule,

if and, applying the Chain Rule to the derivative of the integral,

If is a continuous function and .

then **(Fundamental Theorem, Part I)**

and, if g is differentiable, **(Leibniz' Rule)**