# The Riemann Sum Formula For the Definite Integral

### Part of the Calculus II For Dummies Cheat Sheet

The Riemann Sum formula provides a precise definition of the definite integral as the limit of an infinite series. The Riemann Sum formula is as follows*:** *

Below are the steps for approximating an integral using six rectangles:

Increase the number of rectangles (

*n*) to create a better approximation:Simplify this formula by factoring out

*w*from each term:Use the summation symbol to make this formula even more compact:

The value

*w*is the*width*of each rectangle:Each

*h*value*height*of a different rectangle:So here is the Riemann Sum formula for

*approximating*an integral using*n*rectangles:For a better approximation, use the limit

to allow the number of rectangles to approach

*infinity*: