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**sinewave85** Blood flows through an artery of radius R. At a distance r from the central axis of the artery, the speed of the blood flow is given by S(r)=k(Rē - rē). Show that the average speed of the blood flow is one-half the maximum speed.

My problem is that I can't prove that -- I keep proving that it is two-thirds the maximum speed. Can anyone tell me where I am going wrong?

The maxiumum speed is kRē at r = 0 and the function reaches zero when r = R.

$\displaystyle AverageSpeed = \frac{1}{b-a}\int_{a}^{b}f(x)dx$

$\displaystyle AS = \frac{1}{R-0}\int_{0}^{R}k(R^{2}-r^{2})dr$

$\displaystyle AS = \frac{k}{R}\left(R^{2}r-\frac{1}{3}r^{3}\right)|_{0}^{R}$

$\displaystyle AS=\frac{k}{R}\left(\frac{2}{3}R^{3}\right)$

$\displaystyle AS= (2/3)kR^{2}$

Where did I go wrong? I just can't see it. Thanks for the help!