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A sin^2 and cos^2 integrals question

  1. Aug 30, 2007 #1
    hi!

    1. Is the definite integral over [sin(x)]^2 from 0 to a, is a/2? and also the cosine?

    2. Is it because the average of the sin/cos functions is always 1/2?

    3. and if so, the integration region doesn't matter because the function is positive?
    I mean, what about integration from -a to a?

    4. and from -3a to 0.5a? is it: 0.5*[3.5a]?

    thanks!
     
  2. jcsd
  3. Aug 30, 2007 #2

    dextercioby

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    Well, for 1. why do you ask us ? Can't you compute it all by yourself ? The answer is "no", btw. Then you can figure out the aswers to the other questions. And the average of the sin/cos in not always 1/2.
     
  4. Aug 30, 2007 #3
    are you trying to help?

    I'm asking because I don't know the answers.
     
  5. Aug 30, 2007 #4

    dextercioby

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    Well, the simple calculation of those 2 integrals doesn't yield the results you proposed. So do you know anything about integral calculus ? I'm asking because the answer will make me post the solutions to those integrals or not...
     
  6. Aug 30, 2007 #5
    I've just found a formula on the net for those integrals, thnks anyway.

    but I remember my teacher said that integral over squared(!) sin/cos is always 1/2 or something.
    Is this correct? if so, for what range?
     
  7. Aug 30, 2007 #6

    dextercioby

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    Nope, of course not. The range can be let's say for the cos^2 from 0 to the solution of the equation 2a+sin 2a=2.
     
  8. Aug 30, 2007 #7
    thanks!
     
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