Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Double integral

  1. Dec 3, 2013 #1
    If function is ##f(-x,-y)=f(x,y)##, is then

    ##\int^{a}_{-a}\int^{a}_{-a}f(x,y)dxdy=0##?
    Thanks for answer.
     
  2. jcsd
  3. Dec 3, 2013 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    No, consider for example
    $$\int_{-a}^a \int_{-a}^a x^2 y^2 \, dx dy$$
     
  4. Dec 4, 2013 #3
    Could you tell me some explanation why this is valid only for one integral?
     
  5. Dec 4, 2013 #4

    jgens

    User Avatar
    Gold Member

    The result does not hold for 1-dimensional integrals either. If f(x) = x2, then f(x) = f(-x) and integrating over any interval of the form [-a,a] (where a ≠ 0) gives you a non-zero number.

    If you have a function that satisfies f(-x,y) = -f(x,y) then the integral over [-a,a] × [-a,a] should be zero. So you should probably look for a condition like this.
     
  6. Dec 4, 2013 #5

    Sorry I thought about ##f(-x,-y)=-f(x,y)##

    Is it always valid?
    Also is it valid in case ##f(-x,-y)=f(x,y)## that
    ##\int^{a}_{-a}\int^{a}_{-a}f(x,y)dxdy=2\int^{a}_{0}f(x,y)dxdy##
     
  7. Dec 4, 2013 #6

    lurflurf

    User Avatar
    Homework Helper

    For double integrals there are four cases
    f(x,y)
    f(-x,y)
    f(x,-y)
    f(-x,-y)

    f(-x,-y)=-f(x,y)
    implies that
    f(x,-y)=-f(x,-y)
    thus
    the integral would be zero

    f(-x,-y)=f(x,y)
    implies
    f(-x,y)=f(x,-y)
    ##\int^{a}_{-a}\int^{a}_{-a}f(x,y)dxdy=2\int^{a}_{-a}\int^{a}_{0}f(x,y)dxdy##
     
  8. Dec 4, 2013 #7
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Double integral
  1. Double Integrals (Replies: 1)

  2. A double integral (Replies: 1)

  3. Double Integrals (Replies: 0)

Loading...