In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.
An amusement company maintains records for each video game it installs in an arcade. Suppose that $C(t)$ and $R(t)$ represent the total accumulated costs and revenues (in thousands of dollars), respectively, $t$ years after a particular game has been installed. If
$$
C^{\prime}(t)=2 \quad \text { and } \quad R^{\prime}(t)=9 e^{-0.3 t}
$$
then find the area between the graphs of $C^{\prime}$ and $R^{\prime}$ over the interval on the $t$ axis from 0 to the useful life of the game and interpret the results.
Additional Integration Topics
Area Between Curves