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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


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    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:
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