1. Not finding help here? Sign up for a free 30min 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!

Triple Integral in Cylindrical Coordinates

  1. Nov 9, 2008 #1
    Revised question is below.
     
    Last edited: Nov 9, 2008
  2. jcsd
  3. Nov 9, 2008 #2
    1. The problem statement, all variables and given/known data
    Evaluate [tex]\int\int\int_E{\sqrt{x^2+y^2} dV[/tex] where E is the region that lies inside the cylinder [tex]x^2+y^2=16[/tex] and between the planes z=-5 and z=4.


    2. Relevant equations
    For cylindrical coordinates, [tex]r^2=x^2+y^2[/tex].


    3. The attempt at a solution
    The inside of the integral becomes [tex]\sqrt{r^2}=r[/tex]. Then I integrated using the following bounds: [tex]\int _0^{2*\pi }\int _{-5}^4\int _0^4r drdzd\theta[/tex]

    However, this gives me an answer of [tex]144\pi[/tex]. I've tried several things in Mathematica and I finally tried [tex]\int _0^{2*\pi }\int _{-5}^4\int _0^4r^2drdzd\theta[/tex] which actually gave me the right answer of [tex]384\pi[/tex]. However, integrating over [tex]r^2[/tex] makes no sense.

    Any ideas?
     
  4. Nov 9, 2008 #3

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    The infinitesimal volume element in cylindrical coordinates is [itex]dV=rdrd\theta dz[/itex] not just [itex]drd\theta dz[/itex]
     
  5. Nov 9, 2008 #4
    Thank you for your quick response! I have one more question, though.

    Doesn't the [tex]dr[/tex] take care of the radial component of the volume? Why does it need to be [tex]r dr[/tex]?

    I realize this is a naive question, but I really appreciate your help.
     
    Last edited: Nov 9, 2008
  6. Nov 9, 2008 #5

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    [itex]dr[/itex] does take care of the radial component, but the tangential component is [itex]r d\theta[/itex] not [itex]d \theta[/itex]...remember that the arc length subtended by an angle [itex] \theta[/itex] is [itex]r \theta[/itex]...the same is true for the infinitesimal change in arc length.
     
  7. Nov 9, 2008 #6
    Oh I get it. Thank you so much!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Triple Integral in Cylindrical Coordinates
Loading...