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Trig Substitution easy right?

  1. Nov 9, 2005 #1
    On this physics problem i need to do a double integral (dx,dy) of 1/sqrt(x^2 + y^2 +z^2). Which looks easy enough at first, until I reallized (after many hours) I cannot figure out how to integrate it. I am sure at this point there is some trig substitution (learned too long ago...), but Im basically lost.
     
  2. jcsd
  3. Nov 9, 2005 #2

    dextercioby

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    What's the shape of the domain of integration...?

    If it's a circular one (even the [itex]\mathbb{R}^{2}[/itex] can be thought of as a disk of infinite radius), u can convert to polar plane coordinates...

    Daniel.
     
  4. Nov 9, 2005 #3
    Yah, but its a square sheet. thanks though
     
  5. Nov 9, 2005 #4

    dextercioby

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    In that case, u can depict [itex] y^{2}+z^{2} [/itex] as a constant (wrt "x") [itex] t^{2} [/itex] and use a hyperbolic substitution, in this case

    [tex] x=t\sinh u [/tex]

    and then regroup everything and put "y" back and try to integrate the remaining (only of "y" dependent) function.


    Daniel.
     
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