The velocity v of the flow of blood at a distance r form the central axis of an artery of radius R is
v = k(R^2 - r^2)

Where k is the constant of proportionality. Find the average rate of flow of blood along a radius of the artery. (Use 0 and R as the limits of integration.)

Question

The velocity v of the flow of blood at a distance r form the central axis of an artery of radius R is 
v = k(R^2 - r^2)

Where k is the constant of proportionality. Find the average rate of flow of blood along a radius of the artery. (Use 0 and R as the limits of integration.)

anonymous · Answer

∫ (0, R)

anonymous · Answer

Would I use the velocity formula I am confused because there is not t or time involved to use this function.

dumbcow · Answer

$$avg  = \frac{k}{R} \int\limits_0 ^R R^{2} - r^{2} dr$$

anonymous · Answer

Could you explain this to me please?

anonymous · Answer

This would involve a constant speed k?

dumbcow · Answer

velocity here is given in terms of "r" distance from center of artery
in general to find avg value over interval is:
$$\frac{1}{b-a} \int\limits_a^b f(x) dx$$

anonymous · Answer

Okay thanks I just found this in my book I was unsure. 
Definition of the average value of a function on an interval.
If f is integrable on the closed interval[a, b], then the average value of f on the interval is

dumbcow · Answer

yep, then make sure you treat "R" as a constant