Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles. Give your answer with one decimal place.

Question

 Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles.

Give your answer with one decimal place. 

t(hr) 0 2 4 6 8 10

r(t) (gal/hr) 12.0 10.6 8.8 8.0 6.0 4.8

Answer 1

2·(12+10.6+8.8+8+6) = 90.8 gallons

(Notice the 5 y-values of the rate of change function are used as 5 heights of the rectangles -- the y-value r(10) = 4.8 is NOT used because the left-hand Riemann sum ignores f(b).)

You might consider the following question: Which one word in the question guarantees that this approximation will be the overestimate asked for?