Integral (cos x)^2 dx

  1. Do any one have an idea how to calculate integral of (cos x)^2 ? Or is it even possible? I tried some substitutions and/or rules of trigonometry, like cosxcosx+sinxsinx=1, but it didn't help. Thank you!
     
  2. jcsd
  3. mathman

    mathman 6,471
    Science Advisor
    Gold Member

    cos2x+sin2x=1
    cos2x-sin2x=cos2x
    Therefore cos2x=(1+cos2x)/2

    I'll let you finish.
     
  4. Thank you. :) integral (cos x)^2 dx
     
    Last edited by a moderator: Feb 17, 2008
  5. dont you have to use half angle identities to get integral of cos^2 ?
     
  6. HallsofIvy

    HallsofIvy 40,382
    Staff Emeritus
    Science Advisor

    No, double angle formulas as mathman said.
     
  7. an easy way to remember the solution to this common integral, when integrating over a whole period:

    cos^2 x + sin ^2 x =1
    [tex] \int cos^2 x = \int sin^2 x [/tex]
    , at least when you integrate over a whole period

    [tex] \int cos^2 x + \int sin^2 x =[/tex] length of a period

    so the integral gives length of a period divided by 2
     
  8. Why does this thread have over 16,000 views?

    edit: Oh, it's four years old.
     
  9. First use the half-angle formula to change the cos(x)^2 to (1+cos(2x))/2...
    This will allow you to break the integral into two seperate problems much easier to solve
    integral{ 1/2dx + integral{ cos(2x)dx
    Then you will have x/2 + (sin(2x)/2) + C
     
  10. What the, that's not even correct. If you're gonna revive a 5-year old thread, at least make sure you don't have arithmetic errors.
     
  11. sin(2x)/4 ;)
     
  12. use the euler's formula

    cos x= [e^ix+e^-ix ]
    [-------------]
    [ 2 ]
     
    Last edited by a moderator: Mar 8, 2012
  13. Redbelly98

    Redbelly98 12,036
    Staff Emeritus
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    This is crazy. The very first reply, post #2, answered the question. Six years ago!
     
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