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Tough integration problem

  1. Apr 4, 2004 #1
    Does anyone know how to integrate cos(sqrt x) ?? I know the answer, i need to know the steps to do it?

    Thanks
     
  2. jcsd
  3. Apr 4, 2004 #2

    HallsofIvy

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    Let [itex]u= \sqrt{x}= x^{\frac{1}{2}}[/itex]. Then [itex]du= \frac{1}{2}x^{-\frac{1}{2}}dx[/itex] so that [itex]dx= 2x^{\frac{1}{2}}du= 2udu[/itex].

    [itex]\int{cos(\sqrt{x})dx}= \int{2u cos(u)du}[/itex].

    Now use integration by parts.
     
    Last edited: Apr 4, 2004
  4. Apr 4, 2004 #3

    Dr Transport

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    let [tex] \sqrt{x} = y [/tex] be the variable substution and integrate by parts.
     
  5. Apr 4, 2004 #4

    Dr Transport

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    as I was typing, HallsofIvy gopt it down first.....
     
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