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.
![](/wwtmp/anonymous//images/458936dc-5572-3deb-9965-864c115baa85___0f1ee723-69d2-3187-9fe6-e3704a7e7e88.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.
![](/wwtmp/anonymous//images/458936dc-5572-3deb-9965-864c115baa85___c8ed3299-4d67-32b2-bc61-b3bcabe290f3.png) |
Right endpoint Riemann sum for on |