Answer
$$A = \frac{{64}}{5}$$
Work Step by Step
$$\eqalign{
& {\text{The area of the region enclosed is given by}} \cr
& A = \int_0^8 {\left( {4 - {x^{2/3}}} \right)} \cr
& {\text{Integrating}} \cr
& A = \left[ {4x - \frac{{{x^{5/3}}}}{{5/3}}} \right]_0^8 \cr
& A = \left[ {4x - \frac{{3{x^{5/3}}}}{5}} \right]_0^8 \cr
& A = \left[ {4\left( 8 \right) - \frac{{3{{\left( 8 \right)}^{5/3}}}}{5}} \right] - \left[ {4\left( 0 \right) - \frac{{3{{\left( 0 \right)}^{5/3}}}}{5}} \right] \cr
& {\text{Simplifying}} \cr
& A = 32 - \frac{{96}}{5} \cr
& A = \frac{{64}}{5} \cr} $$
