Results 1 to 3 of 3

Math Help - Triple Integral

  1. #1
    Member
    Joined
    Dec 2009
    Posts
    225

    Triple Integral

    Here's a worked question:



    Shouldn't the second to last line be:

    -3 \int^2_0 \int^3_0 \int^1_0 u^2 du dv dw

    where -3 is the Jacobian? Where did the \frac{1}{3} come from?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by demode View Post
    Here's a worked question:
    Shouldn't the second to last line be:

    -3 \int^2_0 \int^3_0 \int^1_0 u^2 du dv dw

    where -3 is the Jacobian? Where did the \frac{1}{3} come from?
    Haven't done these recently enough to fully check all the steps (without spending a lot of time brushing up), however I can point out that (in the image) the third line up from the bottom has the absolute value of the reciprocal of the expression that came out to -3 above. So the absolute value of the reciprocal of -3 is 1/3. If that's not enough then I'm sure someone else will be able to help you further.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by demode View Post
    Here's a worked question:



    Shouldn't the second to last line be:

    -3 \int^2_0 \int^3_0 \int^1_0 u^2 du dv dw

    where -3 is the Jacobian? Where did the \frac{1}{3} come from?
    It came from the change of bounds. If you go through all the steps, and note the difference in the bounds from before changing to the jacobian to after, you will note that the value makes sense.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triple integral
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 9th 2011, 07:54 AM
  2. Triple integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 18th 2010, 07:02 AM
  3. Double Integral and Triple Integral question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 3rd 2010, 01:47 PM
  4. Triple Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 31st 2009, 05:29 AM
  5. Triple integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 10th 2009, 01:04 PM

Search Tags


/mathhelpforum @mathhelpforum