Calculus(integration): how would i go about solving this problem? would i have to make them equal to each other to find the limits of integration and then subtract the limits from each equation and then each other? in advance!

Judging by the 72 in the bottom right corner of your image, I'm going to assume the answer to my question above is "yes".

First, find the intersections of the parabolas.





Now the area is given by the integral



But over the interval (and just by looking at the graph, you know this), you have , which means



which follows from the definition of absolute value. Then the integral reduces to



Integrating term-by-term yields



as required.

It's going to be the first one...

How you solve this is just insert the number of hours you want for X then solve the equation.

15 * 1 = 15

15 + 30 = 45

15 * 3 =45

45 + 30 = 75