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.
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