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Q regarding Integration

  1. Aug 10, 2004 #1
    Im trying to understand a "simple" identity.

    I have the problem [tex]\ddot{y}+g(t,y)=0[/tex]
    with [tex]y(0)=y_{0}[/tex] and [tex]\dot{y}(0)=z_{0}[/tex]

    What i need to prove is that the solution can be expresed in the form

    Integrating twice is clear that

    Now the book goes

    ???????????????????? How do i prove that? should i do a change of variable? use fubini?

    Im lost, pls help.
  2. jcsd
  3. Aug 10, 2004 #2


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    It is not any change of variables. If you look at the domain of integration in the (s,tau) plane, you will see it is a triangle. All the book is describing is how the triangle is expressed when you switch the order of integration. Fubini's theorem says you can do the switch.
  4. Aug 10, 2004 #3
    Ohhhhhhhhhhhhh.... i know i should have named the tread "stupid Q about integration".
    Thx a lot dood. I sure need to review my calc notes.
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