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How do I integrate sin(x^2) please? Not (sin(x))^2.

  1. Aug 2, 2010 #1
    How do I integrate sin(x^2) please?

    Not (sin(x))^2. Thanks again
     
  2. jcsd
  3. Aug 2, 2010 #2

    Char. Limit

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    Re: Integration

    Use a certain equality of the sine function, namely...

    [tex]sin(u) = \frac{e^{iu}-e^{-iu}}{2i}[/tex]

    Replace u with x^2 and you're good to go, assuming you know erf(x) and erfi(x).
     
  4. Aug 3, 2010 #3

    HallsofIvy

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    Re: Integration

    In other words, the integral cannot be done in terms of elementary functions.
     
  5. Aug 3, 2010 #4

    Char. Limit

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    Re: Integration

    But that's true for most integrals. I used to freak out when I couldn't solve an integral in terms of elementary functions, but I know better now.
     
  6. Aug 4, 2010 #5
  7. Aug 4, 2010 #6

    HallsofIvy

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    Re: Integration

    Actually, it is true for "almost all" functions!:wink:
     
  8. Aug 18, 2010 #7
    Re: Integration

    hey this function is not integerable
     
  9. Aug 18, 2010 #8

    HallsofIvy

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    Re: Integration

    Non-sense. It is continuous, therefore it is integrable. It is simply not integrable in terms of elementary functions.
     
  10. Aug 19, 2010 #9
    Re: Integration

    i only mean that you duffer.it's not easy to integrate
     
  11. Aug 19, 2010 #10

    Char. Limit

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    Re: Integration

    Difficulty really shouldn't matter with integration, I mean, this function isn't easy to integrate either:

    [tex]\frac{sin(x^2) tan(x^3)}{x}+3 x^2 log(x) sin(x^2) sec^2(x^3)+2 x log(x) cos(x^2) tan(x^3)[/tex]

    But we can still express the integral in terms of elementary functions.
     
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