The rectangles in the graph below illustrate a left endpoint Riemann sum for on the interval .
The value of this left endpoint Riemann sum is
,
and this Riemann sum is
the area
of the region enclosed by , the x-axis, and
the vertical lines x = 3 and x = 7.
![](https://wwrenderer-staging.libretexts.org/webwork2_files/tmp/renderer//images/7977d2d3-be28-339d-9c8e-47cc85ba5b87___21831f2d-3359-3e7f-9a76-7d68e16049c5.png) |
Left endpoint Riemann sum for on |
The rectangles in the graph below illustrate a right endpoint Riemann sum for on the interval .
The value of this right endpoint Riemann sum is
,
and this Riemann sum is
the area of the region enclosed by , the x-axis, and the vertical lines x = 3 and x = 7.
![](https://wwrenderer-staging.libretexts.org/webwork2_files/tmp/renderer//images/7977d2d3-be28-339d-9c8e-47cc85ba5b87___00baf3bc-6f42-3345-aa0a-8a2ba4341a1b.png) |
Right endpoint Riemann sum for on |