SCalcET$96\mathrm{.}5\mathrm{.}020.$

The velocity $v$ of blood that flows in a blood vessel with radius $R$ and length $f$ at a distance $r$ from the central axis is

$v(r)=\frac{p}{4l}(R^2-r^2)$

where $P$ is the pressure difference between the ends of the vessel and $$ is the viscosity of the blood. Find the average velocity $v_{\text{a}\text{v}\text{e}}($with respect to $r)$ over the interval $0rR.$

$v_{\text{a}\text{v}\text{e}}=$