Partial values of the function h are given in the table below. Use a midpoint sum with 3 intervals to estimate the area between h and the x-axis on [-2,4] or explain why you can't.
Dividing [-2,4] into 3 sub-intervals gets us sub-intervals [-2, 0], [0,2], and [2,4]. The midpoints of these sub-intervals are -1, 1, and 3. Since the table tells us what h is at these midpoints, we are able to use a midpoint sum as requested.
On [-2,0] we have
On [0,2] we have
On [2,4] we have
Adding the areas of the rectangles we get
12 + 4 + 0 = 16
as our estimate.