Answer
$$\frac{{844}}{5}$$
Work Step by Step
$$\eqalign{
& \int_4^9 {2x\sqrt x } dx \cr
& {\text{multiply}} \cr
& = \int_4^9 {2{x^{3/2}}} dx \cr
& = 2\int_4^9 {{x^{3/2}}} dx \cr
& {\text{find the antiderivative by the power rule}} \cr
& = 2\left( {\frac{{{x^{5/2}}}}{{5/2}}} \right)_4^9 \cr
& = \frac{4}{5}\left( {{x^{5/2}}} \right)_4^9 \cr
& {\text{part 1 of fundamental theorem of calculus}} \cr
& = \frac{4}{5}\left( {{{\left( 9 \right)}^{5/2}} - {{\left( 4 \right)}^{5/2}}} \right) \cr
& {\text{simplify}} \cr
& = \frac{4}{5}\left( {243 - 32} \right) \cr
& = \frac{{844}}{5} \cr} $$
