Answer
The total mass of the rod is $~\frac{140}{3}~kg$
Work Step by Step
We can find the total mass of the rod:
$\int_{0}^{4}\rho(x)~dx$
$=\int_{0}^{4}(9+2\sqrt{x})~dx$
$=(9x+\frac{4x^{3/2}}{3})\vert_{0}^{4}$
$=[9(4)+\frac{4(4)^{3/2}}{3}]+[9(0)+\frac{4(0)^{3/2}}{3}]$
$=(36+\frac{32}{3})+(0)$
$=(\frac{108}{3}+\frac{32}{3})$
$= \frac{140}{3}~kg$
The total mass of the rod is $~\frac{140}{3}~kg$
