The table below gives measured values of the flow rate (in ) of water entering a…
MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
The table below gives measured values of the flow rate W(t) (in m3/h) of water entering a reservoir at various times t (in hours).
t (h)
0
3
6
9
12
W(t)
42
38
34
29
25
(a) Approximate the total volume of water (in m3) that enters the reservoir over the 12-hour interval using four subintervals of equal length and the left endpoints of those subintervals.
(b) Without doing any further numerical calculations, determine whether your approximation in part (a) is an overestimate or an underestimate of the actual volume. Provide a thorough explanation that references relevant features of W.
(c) Suppose the same data were collected every 1.5 hours instead, creating eight equal subintervals on [0,12]. Describe how and why the accuracy of the new left-endpoint estimate would compare with the result from part (a).