Expressing the limits of integration for radius in polar coordinates

[iScience]

i'm trying to integrate some some function bounded by the x-y domain of x²+y²=6y

which is a circle on the x-y plane shifted upward where the outer part of the circle is 6.

i'm trying to integrate a double integral.. ∫∫f(x)rdrdθ

i don't know how to express my limits of integration for r.

the only thing i can think of is going from 3 to 6 but then this means that i have a radius three units long going to a radius of 6 units long. what I'm looking for is a radius 0 units long to radius 3 units long, i just need this shifted up 3 units. how do i express my limits of integration for the r component?

thanks

 

[ehild]

You can choose the origin of he polar system of coordinates at (0,3), and change the variable y to u=y-3 in the integrand.

ehild

 

[LCKurtz]

You don't need to shift the origin. Write the equation $x^2+y^2=6y$ in polar coordinates to get a simple polar equation in the form $r = f(\theta)$, which will give you the $r$ bounds.