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 is the 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:
