Results 1 to 3 of 3

Math Help - Volume integral, how do I find the limits for my integral?

  1. #1
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84

    Volume integral, how do I find the limits for my integral?



    Hi, does anyone know how to find the integral that needs to be evaluated here? I can't understand how to find it from the region

    thanks in advance!

    from here, not take home test, sheet 3
    http://www.maths.ox.ac.uk/courses/course/12489/material
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by LHS View Post


    Hi, does anyone know how to find the integral that needs to be evaluated here? I can't understand how to find it from the region

    thanks in advance!

    from here, not take home test, sheet 3
    Course Material for Calculus in Three Dimensions and Applications | Mathematical Institute - University of Oxford
    Use the change of coordinates

    u=yz \quad v=xz \quad w =xy

    Solving for x, y and z gives

    x=\sqrt{\frac{vw}{u}} \quad y=\sqrt{\frac{uw}{v}}  \quad z=\sqrt{\frac{uv}{w}}

    This has Jacobian

    J=\begin{vmatrix}0 & z & y \\ z & 0 & x \\ y & x & 0 \end{vmatrix}=2xyz

    So this gives that

    dudvdw=2xyzdxdydz \iff dxdydz=\frac{dudvdw}{2\sqrt{uvw}}

    Now you have the integral

    \iiint 1 dxdydz= \int_{a^2}^{b^2} \int_{a^2}^{b^2} \int_{a^2}^{b^2} \frac{dudvdw}{2\sqrt{uvw}}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84
    Awesome! But I am confused how you obtained that jacobian, dx/du isn't equal to zero

    Edit: Ah.. I see what you're doing, thanks, that's all sorted now
    Last edited by LHS; May 18th 2011 at 03:22 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triple integral to find volume
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 10th 2011, 01:07 AM
  2. Using integral to find volume problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 7th 2011, 01:48 PM
  3. Find limits for integral
    Posted in the Calculus Forum
    Replies: 12
    Last Post: March 31st 2011, 08:33 AM
  4. Find the Volume, Triple Integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 6th 2010, 05:50 AM
  5. Use triple integral to find volume
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 6th 2008, 02:00 PM

Search Tags


/mathhelpforum @mathhelpforum