Estimate the area under the curve f(x) = 16 – x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles. Answer to the nearest integer.

Answer 1

16-x^2 is concave down, so you want to use the right endpoints. Each interval has width 1, so you just have

2(f(1)+f(2)+f(3)) = 2(15+12+7) = 68

There are several good online Riemann Sum calculators. You can use them to verify your work.

Answer 2

39