The rate (in liters per minute)

Question

t min	0	0.5	1	1.5	2	2.5	3
l/min	40	38	36	34	32	30	28

Answer: ? liters.

The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals. Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 min.

Answer 1

We are calculating the average of the left- and right-hand Riemann sums, which also equals the trapezoidal sum. There are 6 1/2-minute time intervals, so we are summing the areas of 6 rectangles, each of which is 1/2 wide. The heights will be the average of the y-values of the rate function at the endpoints of these subintervals: thus, we calculate the height of the first rectangle by taking (40 + 38) / 2 = 39.

A = 1/2 (39 + 37 + 35 + 33 + 31 + 29) = 102 liters