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Tricky integral (how to solve)?

  1. Jun 22, 2005 #1
    I attached this integran (see picture). If I put this in my calculater he doesn't give me a formula independant of other integrals. Is this unsolveable? For you informations, C is a constant.

    Attached Files:

  2. jcsd
  3. Jun 22, 2005 #2
    hello there

    in your diagram the intergrand is not being integrated dy and dx should be placed after
    the intergrand, correct me if im wrong

  4. Jun 22, 2005 #3


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    That's a common notation especially when the integrals are nested (folded) deep. It's just:

    [tex]\int\int \sqrt{x^2+y^2+C}dydx[/tex]
  5. Jun 22, 2005 #4


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    Do you know how to integrate:

    [tex]\int \sqrt{t^2 + c} \, dt[/tex]

    If you can do that the rest is pretty simple.
  6. Jun 22, 2005 #5
    no, sorry I don't know how to integrate this. Can someone tell me please?
  7. Jun 22, 2005 #6
    hello there

    just make a substitution which forms a change of variable such that you get something much more simpler in which you are able to integrate, as for your double integral, once you have put the intergrand in the correct position you first integrate the inside then you will be left with one integral and then integrate the next, but for each integral you are only integrating with respect to one variable and so all other variables are treated as constants in the intergrand

    take care

  8. Jun 22, 2005 #7
    Ok, I'll try it.
  9. Jun 29, 2005 #8
    integrate it by the lebniz product rule. take one function as sqrt(t2 + c) and the other as one.
  10. Jun 29, 2005 #9


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    Yes,it's reccomendable to use part integration,because the sign of the unknown constant can be either plus or minus and one wouldn't know which sub (cosh or sinh) to make.

  11. Jun 29, 2005 #10
    You left of a square, it was actually

    [tex]\int\int \sqrt{x^2+y^2+C^2}dydx[/tex]

    which makes it easier (C^2 is nonzero).
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