Integrating in the cylindrical coordinate system

Hi everyone please see the problem below:

http://img515.imageshack.us/img515/6356/img0743br.jpg

Im trying to learn how to evaluate 3a. NOTICE: ap is a vector(boldfaced). My prof vagely mentioned something about not being able to integrate directly since as the direction of phi chances so does the direction ap. I know this seems unclear as this has me confused aswell and i cant find any information in my text regarding this. Can someone please help me understand how to integfrate this?

(p, phi , z)

p = radial distance from z-axis

phi = angle in radians meansured from "x-axis"

z=z as in cartesian.

Thank you!

Re: Integrating in the cylindrical coordinate system

I should also add, this has applications in field Theory or Electromagnetics if that help clarify the question.

Re: Integrating in the cylindrical coordinate system

Is anyone able to suggest anything I can read for the above problem?

Re: Integrating in the cylindrical coordinate system

Not without knowing what $\displaystyle a_\rho$ is!

Re: Integrating in the cylindrical coordinate system

Quote:

Originally Posted by

**HallsofIvy** Not without knowing what $\displaystyle a_\rho$ is!

ap is the vector pointing in the p direction, where:

(p, phi , z)

p = radial distance from z-axis

phi = angle in radians meansured from "x-axis"

z=z as in cartesian.

Re: Integrating in the cylindrical coordinate system

Is anyone able to suggest anything I can read for the above problem?