Answer
$\frac{32}{3}$
Work Step by Step
Set up the integration to find the area bounded by the graphs of the equations.
y=0 when x=0 and x=4, so the limits of integration are 0,4
$\int_0^4 (-x^2 +4x)dx$, Integrate
$ [-\frac{1}{3}x^3 +2x^2]_0^4$ , Evaluate the definite integral
$(-\frac{64}{3} +32) - (0)$, Simplify
$\frac{32}{3}$
