# Riemann Sum of Function Left Approximation

What is the left Riemann sum from 0 to 4, with n = 4, of the function:

Draw a picture and divide the area into n equal width rectangles. Set up the initial equation.

Expand the summation. Since we are using the left approximation method we are using the left point of each rectangle for the height.

Calculate the width of each rectangle.

Calculate the height of each rectangle:

First rectangle

Second rectangle.

Third rectangle.

Fourth rectangle.

Substitute widths and heights back into original equation and simplify.

The Riemann sum, or the area under the function from 0 to 4 is approximately 10. If we wanted a more accurate approximation of the area, we could increase n to a larger number.