1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral (cos x)^2 dx

  1. Apr 28, 2004 #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. Apr 28, 2004 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

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

    I'll let you finish.
     
  4. Apr 28, 2004 #3
    Thank you. :) integral (cos x)^2 dx
     
    Last edited by a moderator: Feb 17, 2008
  5. Mar 3, 2008 #4
    dont you have to use half angle identities to get integral of cos^2 ?
     
  6. Mar 3, 2008 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, double angle formulas as mathman said.
     
  7. Mar 5, 2008 #6
    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. Mar 5, 2008 #7
    Why does this thread have over 16,000 views?

    edit: Oh, it's four years old.
     
  9. Sep 13, 2009 #8
    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. Sep 13, 2009 #9
    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. Sep 14, 2009 #10
    sin(2x)/4 ;)
     
  12. Feb 22, 2010 #11
    use the euler's formula

    cos x= [e^ix+e^-ix ]
    [-------------]
    [ 2 ]
     
    Last edited by a moderator: Mar 8, 2012
  13. Feb 22, 2010 #12
  14. Feb 22, 2010 #13

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    This is crazy. The very first reply, post #2, answered the question. Six years ago!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Integral (cos x)^2 dx
  1. Integral of cot(x)^2 dx (Replies: 22)

Loading...