MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
A water tank is being filled, and the inflow rate f(t) (in liters per minute) is measured at irregular times t (in minutes) after filling begins.
t (min)
0
3
7
11
15
22
f(t) (L/min)
18
23
29
34
37
38
(a) Using the data and assuming the flow rate varies linearly between each pair of successive measurements, approximate the volume of water, in liters, that enters the tank during the first 22 minutes.
(b) Compute the average inflow rate, in liters per minute, over the 22-minute interval using your result from part (a).
(c) Explain how the non-uniform spacing of measurement times affects the numerical work required in part (a) compared with the case of equally spaced data.