Oil is being pumped out of a well at a rate of ft400t28t32 w

Oil is being pumped out of a well at a rate of

f(t)=400/(t^2-8t+32)

where f(t) is the rate at time t in hours. The total amount of oil that is pumped from the well in 12 hours is estimated in four different ways: Using n = 3, n = 6, n = 12 and n = 24 intervals of equal width. In each case the midpoint is used. The area that represent each of these estimates are shown in the figures below.

Which of the estimates gives the worst approximation?

Which of the estimates gives the best approximation?

Solution

(a) In first option we can see that there are very less segments of rectangles divided. So the worst espimation would be given by the first one.

(b) Maximum segments are divided in last option. so it will give best approximation off the area.