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Cos^2(x) Integral

  1. Apr 12, 2012 #1
    1. The problem statement, all variables and given/known data
    [itex]\int cos^{2}x dx[/itex]

    I know that

    [itex]cos^{2}x = \frac{1+cos2x}{2}[/itex]

    but I don't see how that helps me.
    Can someone help walk me through it..

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 12, 2012 #2
    Well, that leaves you with:
    [tex]\int \frac{1}{2}+\frac{1}{2}cos(2x)dx[/tex]

    Which you can break up into two integrals:
    [tex]\int \frac{1}{2}dx + \int \frac{1}{2}cos(2x)dx[/tex]

    The first one should be no problem. Isn't there some sort of substitution you can make for the second one?
     
  4. Apr 12, 2012 #3

    Dick

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    Can you integrate cos(2x)? Use a u substitution.
     
  5. Apr 12, 2012 #4
    u=2x du=(1/2)dx
    (1/2)∫cosudu
    =(1/4)sin2x

    So then..
    x/2 + (1/4)sin2x
    but thats not the answer..
     
    Last edited: Apr 12, 2012
  6. Apr 12, 2012 #5

    Dick

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    I think it is the correct answer. You should probably put a +C on it. Is that the problem?
     
  7. Apr 12, 2012 #6
    Oh nevermind was looking at the wrong answer. Thanks for the help.
     
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