Answer
$\frac{8}{3}$
Work Step by Step
Set up the integration to find the area bounded by the graphs. y=0 when x=0, and x=4, so we use those as our limits of integration
$\int_0^4 (2\sqrt x -x)dx$, Integrate
$[\frac{4}{3}x^{\frac{3}{2}} - \frac{1}{2} x^2]_0^4$, Evaluate the definite integral
$(\frac{32}{3} - 8) - (0)$, Simplify
$\frac{8}{3}$
