Answer
$$\eqalign{
& \left( {\text{a}} \right){\text{Graph}} \cr
& \left( {\text{b}} \right){\text{The integrand does not have an elementary antiderivative}} \cr
& \left( {\text{c}} \right)A \approx 4.7721 \cr} $$
Work Step by Step
$$\eqalign{
& y = \sqrt {\frac{{{x^3}}}{{4 - x}}} ,{\text{ }}y = 0,{\text{ }}x = 3 \cr
& \cr
& \left( {\text{a}} \right){\text{Graph shown below}} \cr
& \cr
& \left( {\text{b}} \right){\text{From the area shown below we can define the area of}} \cr
& {\text{the region as:}} \cr
& A = \int_0^3 {\sqrt {\frac{{{x^3}}}{{4 - x}}} } dx \cr
& {\text{Simplifying}} \cr
& A = \int_0^3 {\frac{{\sqrt {{x^3}} }}{{\sqrt {4 - x} }}} dx \cr
& A = \int_0^3 {\frac{{x\sqrt x }}{{\sqrt {4 - x} }}} dx \cr
& {\text{We can see that the area of the region is difficult to find by }} \cr
& {\text{hand because we cannot apply substitution or other method}} \cr
& {\text{the integrand does not have an elementary antiderivative}}{\text{.}} \cr
& \cr
& \left( {\text{c}} \right){\text{ From the graphing utility we can approximate the area}} \cr
& A \approx 4.7721 \cr} $$
