Measurements of a lake’s width were taken at 15-foot intervals, as shown:

Question

x= 0 15 30 45 60 75 90 105 120
f(x)= 0 15 18 20 19 23 24 22 12
Estimate integral (0,120) f(x) dx with n = 4, using the left-hand approximation, the right hand approximation, and the trapezoidal approximation.

I figured out the midpoint approximation but I need some guidance with these other approximations.

Answer 1

If you can do the midpoint you can do the rest. Draw pictures.