Riemann Sum

Riemann Sum is a method for approximating the area underneath a continuous function. To find the Riemann’s sum, divide the area under the curve into n equal width rectangles. Then calculate the area of each rectangle and sum the results together. This is described by the equation below:

The variable represents the approximated area in the range , the expression represents the height of each rectangle and represents the width of each rectangle also called the change in x. The symbol Σ (capital sigma) represents the summation operator which sums the expression starting from and ending at , incrementing by one at each step.

Left Riemann Sum Approximation

Note: This image shows the left approximation method, see the interactive above for the alternative methods: mid-point, right, and trapezoid.