# First fundamental theorem of calculus modules

## Overview

After completing this section, students should be able to do the following.

- Define accumulation functions.
- Calculate and evaluate accumulation functions.
- State the First Fundamental Theorem of Calculus.
- Take derivatives of accumulation functions using the First Fundamental Theorem of Calculus.
- Use accumulation functions to find information about the original function.
- Understand the relationship between the function and the derivative of its accumulation function.

# What's in a calculus problem?

## Ximera Module

Two young mathematicians discuss what calculus is all about.

# The First Fundamental Theorem of Calculus

## Ximera Module

The rate that accumulated area under a curve grows is described identically by that curve.