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 A represents the approximated area, f(xi) represents the height of each rectangle and dx (the change in x), represents the width of each rectangle. The symbol Σ means add all of the parts together.

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


Riemann Sum of Function Left Approximation

To calculate the Riemann sum of a function using the left approximation method. negative x squared plus four x from zero to four using the left approximation method.

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Integral | concept