# Fundamental Theorem of Calculus

5 videos

1 skill

The very powerful and very surprising fact at the heart of calculus is that integrals and derivatives are, in a sense, opposite to one and other. At first glance, rates of change and slope might seem completely unrelated to the area under a curve. In this tutorial, you will learn about the aptly named "Fundamental theorem of calculus".

### Fundamental theorem of calculus

VIDEO
8:03 minutes

The fundamental theorem of calculus shows how, in some sense, integration is the opposite of differentiation.

### Applying the fundamental theorem of calculus

VIDEO
3:54 minutes

See what the fundamental theorem of calculus looks like in action.

### Slightly trickier fundamental theorem problem

VIDEO
3:00 minutes

Sometimes you need to swap the bounds of integration before applying the fundamental theorem of calculus.

### Both bounds being a function of x

VIDEO
5:04 minutes

How do you apply the fundamental theorem of calculus when both integral bounds are a function of x.