Estimate the area under the graph with midpoint?

Question

 Estimate the area under the graph of f(x) = 16 - x^2 from x=0 to x=4 using 4 approximating rectangles.

I got the right sum = 34 and left sum = 50 but how do I estimate area with midpoints?

Answer 1

Use the midpoints to find the "height" of the rectangle.

The first midpoint is 0.5, f(0.5) = 15.75 so the area of the first rectangle is (15.75)(1) = 15.75