There has been a few times when I switch from Cartesian to cylindrical coordinates to integrate I would get the wrong because I used the wrong substitution. 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?