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# Find a constant so the area between two graphs has specified area

For a constant define Find the values for such that the region above the graph of and below the graph of has area equal to .

We consider three cases: , and .
Case 1: . This is not possible since if then and so the area above the graph of and below the graph of is equal to Case 2: . If then on , so we have the area, , of the region between the two graphs given by Setting this equal to and solving for we have Case 3: . If then on so Setting this equal to and solving for we obtain Thus, the possible values of to make the area of the region above the graph of and below the graph of are .

1. Edwin says:

Hi! Quick question, how did you know that the interval was when ?

• RoRi says:

Hi! Since we want to look at the area below and above we want the interval to correspond to where . So, we look for We have equality if . If then this gives us . Since we have in this case by assumption, we know so the interval is . So we have when .