Partial values of the function f ( x ) are given in the table below. Use a midpoint sum with 4 equal sub-intervals to estimate the area between f and the x-axis on [0,1], or explain why you can't.
Dividing [0,1] into 4 equal sub-intervals gets us the sub-intervals [0,0.25], [0.25, 0.5], [0.5,0.75], and [0.75,1]. The midpoints of these sub-intervals are
0.125, 0.375, 0.625, and 0.875.
The table doesn't tell us what f is at these points, so we can't use the requested midpoint sum.