Integral Question

  • Thread starter ehrenfest
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  • #1
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Homework Statement


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]"

Homework Equations





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.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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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)?
 
  • #3
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That makes sense. :biggrin:
 

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