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!

Integral Question

  1. Jul 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Can someone explain to me the logic of this statement:

    "Since the value of f (x, y) is unchanged when we swap x with y,

    [tex]\int_0^1 \int_0^x f (x+y)dydx = 1/2 \int_0^1 \int_0^1 f (x+y)dydx.[/tex]"

    2. Relevant equations

    3. The attempt at a solution

    [tex]\int_0^1 \int_0^x f (x+y)dydx = \int_0^1 \int_0^y f (y+x)dxdy[/tex]

    But I do not think that is the same.
  2. jcsd
  3. Jul 30, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Draw a picture of the region of integration. It's one half of the unit square. What is the integral over the other half equal to if f(x,y)=f(y,x)?
  4. Jul 30, 2007 #3
    That makes sense. :biggrin:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integral Question
  1. Integral Questions (Replies: 2)

  2. Integration question (Replies: 2)

  3. Integral Question (Replies: 5)

  4. Integral Question (Replies: 8)

  5. Integration Question (Replies: 4)