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.libretexts.org/webwork2_files/tmp/renderer//images/841b27c2-61c8-3252-beea-caad5748ce99___3f74726f-c6d8-3f98-81d5-2b8fe9ad7b7c.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.libretexts.org/webwork2_files/tmp/renderer//images/841b27c2-61c8-3252-beea-caad5748ce99___8a2e0be2-8a69-351f-862b-656d93511530.png) |
Right endpoint Riemann sum for on |