How Do You Determine the Limits for r and θ in a Cylindrical Coordinate System?

[J Galt]

What are the r and θ limits for the triple integral of y where there's a parabloid cylinder x=y^2 and planes x+z=1 and z=0?

I rearranged x+z=1 to get z=1-x => so 1-rcosθ; 0 ≤ z ≤ 1-rcosθ
but I don't know how to get the limits for θ or r. How do I do this?

 

[tiny-tim]

Welcome to PF!

Hi J Galt! Welcome to PF!

(are you trying to find the volume … you didn't say?)

Just because there's a cylinder, that doesn't mean you have to use cylindrical coordinates.

Use whatever method makes it easier!

In this case, I'd use horizontal (z = constant) slices, 'cos I think that's easiest!