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 what is the area found using midpoints? How do I do it?

Answer 1

Using midpoints, your x's would be
x = .5, 1.5, 2.5, and 3.5
f(.5) = 16 - .25 = 15.75
f(1.5) = ... = 13.75
f(2.5) = ... 9.75
f(3.5) = ... = 3.75
the width of each rectangle is still 1

area = 1*(15.75+13.75+9.75+3.75) = 43