The shaded region between the graphs of $\displaystyle {y}=-{2}{x}^{{2}}+{20}$ and $\displaystyle {y}={3}{x}-{15}$ is displayed below in orange.


The shaded region lies between $\displaystyle {x}=$ and $\displaystyle {x}=$ .

A typical rectangle is shown in the diagram located at position x. What is the area of this rectangle, in terms of $\displaystyle {x}$?
$\displaystyle \Delta{x}$ Preview Question 6 Part 3 of 4  

Now find the total area of the orange shaded region. Write your answer in exact form.

$\displaystyle {A}=$
Preview Question 6 Part 4 of 4