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/262acf07-c2f1-36e9-8ca0-8f2e2f2acbba___a3b1c6e8-3c3e-3798-be20-b4c02ec01799.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/262acf07-c2f1-36e9-8ca0-8f2e2f2acbba___2f021b8a-e365-32b4-ac48-67637441d95c.png) |
Right endpoint Riemann sum for on |