Answer
$6 \frac{kg}{m}$
Work Step by Step
We calculate the average density as follows:
$\rho_{avg} = \frac{1}{8-0}\int_{0}^{8}(\frac{12}{\sqrt{x+1}})dx$
$= \frac{3}{2}\int_{0}^{8}\frac{1}{\sqrt{x+1}}dx$
$= \frac{3}{2}[2\sqrt{x+1}]_{0}^{8}$
$= \frac{3}{2}[(2\sqrt{8+1})-(2\sqrt{0+1})]$
$= \frac{3}{2}[6-2]$
$= 6\frac{kg}{m}$
