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.

Question

t (hr) 0 2 4 6 8 10
r(t) (gal/hr) 8.7 7.6 6.8 6.2 5.7 5.3

Answer 1

since the width of each rectangle is 2, the sum is just

2(f(0)+f(2)+...+f(8))

since we're using left-side values.