Integration Problem for Calculus Homework

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January 21st 2009, 10:33 PM
justaguy

Integration Problem for Calculus Homework

I'm having trouble with the following problem from my homework for a Calc. II course:

Quote:

The velocity v of the flow of blood at a distance r from 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.)

Any help would be really appreciated, thanks.

EDIT: I should probably clarify: I know how to use integration in order to find the average value of a function over a range. It's integrating the function that I'm stuck on.
January 21st 2009, 11:55 PM
Jhevon

Quote:

Originally Posted by justaguy

I'm having trouble with the following problem from my homework for a Calc. II course:
Any help would be really appreciated, thanks.

EDIT: I should probably clarify: I know how to use integration in order to find the average value of a function over a range. It's integrating the function that I'm stuck on.

what problems are you having?

the integral is: $\frac 1R \int_0^R k(R^2 - r^2)~dr$

it is a matter of using the power rule for integrals, nothing too fancy. remember, R and k are constants, r is the variable
January 22nd 2009, 12:06 AM
justaguy

Quote:

Originally Posted by Jhevon

what problems are you having?

the integral is: $\frac 1R \int_0^R k(R^2 - r^2)~dr$

it is a matter of using the power rule for integrals, nothing too fancy. remember, R and k are constants, r is the variable

. . . I was assuming R was a variable. This makes more sense now. Thanks.