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For instance I would use x = rcos(θ) and y = rsin(θ) where r and θ are variable when I was suppose to leave r as a constant.

Question: correct me if I am wrong, I should use x = rcosθ and y = rsinθ where r is variable if the cross section parallel to my region of integration are circles whose radius are not constant. For example: a cone.

And I would choose r to be the appropriate constant if the cross sections are circles with constant radius for example the surface x^2 + y^2 = 16 ... a cylinder.

Is there anything else I should know?