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!

Another Double Integral

  1. Jul 4, 2013 #1


    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    Find the volume of the region common to the intersecting cylinders ##x^2 + y^2 = a^2## and ##x^2 + z^2 = a^2##.

    3. The attempt at a solution

    I am totally stuck here. What do they mean when they say 'intersecting cylinders'? I've drawn graphs of circles of radius a, centred at the origin, in the x-y plane and the x-z plane. I've put them together and ended up with two identical circles cutting each other at right angles, and I don't see any cylinders... can anyone help me visualise this?

    They have ended up with

    [tex]8 \int_{x=0}^{a} \int_{y=0}^{\sqrt{a^2 - x^2}} z dy dx[/tex]

    I can understand where the limits of integration come from, but not the factor of 8, nor what is actually going on here...
  2. jcsd
  3. Jul 4, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  4. Jul 4, 2013 #3


    User Avatar
    Gold Member

    Thanks -- a picture really helped. I found it impossible to visualise.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Another Double Integral Date
Jacobian of a coordinate system wrt another system Feb 9, 2018
Another simple double integral Jun 18, 2016
Another double integral problem Jan 6, 2010
Another double integral question Jul 12, 2008
Another Polar Double Integral Nov 24, 2006