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Homework Help: Integration problem

  1. Oct 26, 2008 #1
    Integral of cos√x



    We are supposed to use substitution and integration by parts but I really don't know where to even start.



    No matter what I substitute for U I will be left without a du.
     
  2. jcsd
  3. Oct 26, 2008 #2

    gabbagabbahey

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    what are your limits of integration?...what does your integral become when you use the substitution u=sqrt(x)? What is du?
     
  4. Oct 26, 2008 #3
    There are no limits it is indefinite. If you let U= √x then du= 1/2√x and that is my problem because I am left with with integral of cos(u) and no du.
     
  5. Oct 26, 2008 #4

    gabbagabbahey

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    doesn't [itex]du=\frac{1}{2\sqrt{x}}dx[/itex] and doesn't that mean that [itex]dx=2 \sqrt{x} du= 2udu[/itex]?
     
  6. Oct 26, 2008 #5
    Yes it does. So does that mean when I integrate I get u^2 sinu and from there I just need to back substitute?
     
  7. Oct 26, 2008 #6

    gabbagabbahey

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    Well, that means that

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

    now you'll need to integrate by-parts....try using f(u)=2u and g'(u)=cos(u)du
     
  8. Oct 26, 2008 #7
    oh ok. Thank you for the help.
     
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