Difficult Math Question?

[aa11]

Is it possible to set up a double integral in polar coordinates over the region of a circle that is located away from the origin and the x and y axis? If so, how do I set up the limits of integration for the double integral?


(x and y axis origin)
-------------X










-------------------------------------------------------------------(circle boundary point)------(center of circle)
----------------------------------------------------------------------------------------X------------------------X

This problem is not the same as the common easy problems involving double integrals and circles. Thanks for your help.

 

[aa11]

I have a good idea for the theta limits of integration but not sure about the r limits of integration.

 

[C1]

It's been a long time for calculus, but you would think that one limit for f(x,y) for dA translated to polar would be theta & the other would be r.

Seems the integral for this solution might be found in one of the math handbooks on integral formulas.

http://tutorial.math.lamar.edu/Classes/CalcIII/DIPolarCoords.aspx