Please help me out with math, thank you

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

Options:

1)	2.742
2)	21.2
3)	32.9
4)	None of these

Answer 1

R₅ = 5.0(2 - 0) + 2.0( 5 - 2) + 1.2(7 - 5) + 0.6(11 - 7) + 0.4(12 - 11) = 21.2

Answer is 2)

Answer 2

With right reimann sums, we estimate the area under the curve by creating rectangles over each interval, where the height of each rectangle is the right point for each interval.

This means our heights are going to be 5.0, 2.0, 1.2, 0.6, and 0.4

And our widths will be the delta x's, so 2, 3, 2, 4, and 1 (x_n+1-x_n for each x_n)

Area = 5.0*2 + 2.0*3 +1.2*2 + 0.6*4 + 0.4*1 = 21.2

Answer 3

Check out the video for alternative ways to visualize the problem.