# 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.

### Proof of fundamental theorem of calculus

VIDEO 14:00 minutes
See why this surpising result is true.

### Fundamental theorem of calculus

PRACTICE PROBLEMS
Fundamental theorem of calculus practice problems