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Integration question

  1. Apr 15, 2007 #1
    I would appreciate a hint as how to integrate the following, after some thought, I used Taylor series and integrated in term.

    Thanks

    [tex]\int\sin{x^2}[/tex]
     
  2. jcsd
  3. Apr 15, 2007 #2

    cristo

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    Use the identity [itex]\sin^2x=\frac{1}{2}(1-\cos(2x))[/itex]. This is derived from the double angle formula for cosine; [itex]\cos(2x)=\cos^2x-\sin^2x=1-2\sin^2x [/itex]. Rearranging gives the result.
     
  4. Apr 15, 2007 #3

    mathwonk

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    sin(x^2) apparently has no elementary integral. hence a taylor series is about all you can do. a discussion of such questions is in a paper on brian conrad's page at umichigan.

    sin^2(x) of course does have, as can be seen by using integration by parts, or the trig identity suggested above.
     
    Last edited: Apr 15, 2007
  5. Apr 15, 2007 #4

    cristo

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    Sorry... I misread it as sin^2(x)!
     
  6. Apr 15, 2007 #5

    Gib Z

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    Good Work, Thats the best you can do.
     
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