Results 1 to 4 of 4

Math Help - reversing order of integration

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    7

    reversing order of integration

    hi how do you know for 0 to 2 (1st int) and x^2 to 2x (2nd int) (x^3) dydx if you should have x now going from 0 to y^.5 or 0 to y/2 and likewise y going from 0 to 2x or 0 to x^2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by candi View Post
    hi how do you know for 0 to 2 (1st int) and x^2 to 2x (2nd int) (x^3) dydx if you should have x now going from 0 to y^.5 or 0 to y/2 and likewise y going from 0 to 2x or 0 to x^2?
    Have you drawn a sketch of the region of integration?

    It is very clear from such a sketch that the reversed integral limits are x = y/2 to x = +\sqrt{y} and y = 0 to y = 4:

    I = \int_{y=0}^{y=4} \int_{x = y/2}^{x = \sqrt{y}} x^3 \,dx \, dy.
    Last edited by mr fantastic; March 8th 2008 at 08:10 PM. Reason: Fixed a small bit of latex
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    7
    i did draw a sketch. and the graphs are both at the origin. but i'll look at what you wrote again to see if i'll understand it better. thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    It's pretty clear having a sketch, you'll see mr fantastic's result is correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 8th 2011, 04:59 PM
  2. Reversing the order of integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 3rd 2010, 01:51 AM
  3. Replies: 1
    Last Post: April 29th 2010, 08:42 PM
  4. Replies: 6
    Last Post: August 8th 2008, 04:37 AM
  5. Replies: 4
    Last Post: March 8th 2008, 05:29 PM

Search Tags


/mathhelpforum @mathhelpforum