Let

Find the area between the graphs of and on the interval .

First, we draw the graph, shading the region between the two graphs in blue.

For this exercise, since and cross in the interval we are interested (and we are calculating the area between the graphs, so we’re really looking at the integral of ) we split the integral into two pieces (at the point the functions cross).

We’ve already computed these integral in the previous two exercises (here and here). Using the results of those exercises we then have,