The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12.

Question

The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12.

Using a right Riemann sum with 5 subintervals estimate the total amount of water consumed in that time interval. 

x. 0, 2, 5, 7, 11, 12

f(x)

5.7

5.0

2.0

1.2

0.6

0.4

a)2.742

b)21.2

c)32.9

d)None of these

Answer 1

A right Riemann sum means that you sum together the areas of rectangles whose heights are determined by the right side of the rectangle. So the first rectangle has a width of 2 and a height of 5.0, which works out to an area of 10. The second has a width of 3 and a height of 2.0, with an area of 6. The third has a width of 2 and a height of 1.2, with an area of 2.4. The fourth has a width of 4 and a height of 0.6, with an area of 2.4. The fifth has a width of 1 and a height of 0.4, with an area of 0.4.

The sum of the area of these rectangles is 21.2.