Calculus integration with a graph

Question

The exact question is:

Suppose that one of the industrial plants increases its water consumption between 9:00 A.M. and 10:00 A.M. and that the rate at which the reservoir supplies water increases linearly, as

shown in the figure. How much water does the reservoir supply during that 1−hour time period?

The graph that goes with the question has r(gallons/min) as the y-axis and minutes as the x-axis. I was told that I just needed the area under the curve but that doesn't make sense to me. Doesn't the graph equate to gallons/min^2 ? And since we need just gallons shouldn't it be integrated twice ?

Answer 1

No, I think you misunderstand the graph (although you have not supplied it).

The RATE of water supply varies with time and the volume supplied is given by integration.

Two thoughts may help you.

1> If the graph were a straight horizontal line, what would you do to get the volume supplied?

2> In effect this is similar to a vehicle which is accelerating. How do you find the distance traveled over time? Yes, integrate!