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.
In this problem on the entire interval ; however, the function is defined piecewise on this interval as
Thus, we break the integral into intervals and , and in both cases we are taking the integral of , but the definition of will depend on which interval we are in. The computation is as follows:
you could have translated the graph 1unit to the left , and it would be the same as problem 11