1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Limits of integration question (double integral)

  1. Dec 9, 2013 #1
    so in the image in the link below, i don't understand a couple of things:

    1.) the center of the cylinder is off to the side and not at the center. where/how in the problem are we taking this into account? because it should definitely affect the volume under the parabaloid right?

    2.) most of the other times i've worked with circles/cylinders/spheres in polar coordinates i'ved always used 0≤θ≤2[itex]\pi[/itex] as my limits of integration for theta. what's with the [itex]\frac{-\pi}{2}[/itex]≤θ≤[itex]\frac{\pi}{2}[/itex] limits? ie why am i only integrating half of the circle?

    3.) r=2cosθ??... where did this come from?..


    (i don't know how to make the image smaller on here using the so i just posted the site)
  2. jcsd
  3. Dec 9, 2013 #2


    User Avatar
    Gold Member

    The ranges of r and θ are affected by this shift, as you have noticed below.

    It does not represent half of the circle, but rather all of it. How is θ defined?
    This comes about from the projection of the intersection of the cylinder and the paraboloid onto the xy plane.

    I think I had a question like this in my exam last year.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted