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 it is
[select an answer]
an overestimate of
equal to
an underestimate of
there is ambiguity
the area of the region enclosed by , the x-axis, and the vertical lines x = 2 and x = 6.
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 it is an
[select an answer]
an overestimate of
equal to
an underestimate of
there is ambiguity
the area of the region enclosed by , the x-axis, and the vertical lines x = 2 and x = 6.
Right endpoint Riemann sum for on
Using left and right Riemann sums based on the diagrams above, we definitively conclude that
Hint: For the last integral, you should consistently choose either to underestimate or overestimate the area. This may require that you use the left Riemann sum for some x-intervals and the right Riemann sum for other x-intervals.