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Integrate sinx*cox* using double angle

  1. Aug 5, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫ Sinx cos x dx

    2. Relevant equations



    3. The attempt at a solution
    If you integrate it using substitution, you get -cos2(x)/2but if you use double angle formula to rewrite the problem, it will be ∫1/2 sin(2x), and integrate it, you get -cos(2x)/4. isn't it weird?
     
  2. jcsd
  3. Aug 5, 2013 #2
    You are forgetting that each of those two integrals must have ##+ C## appended to it. Now recall that ## \cos 2x = 2 \cos^2 x - 1 ##.
     
  4. Aug 5, 2013 #3

    D H

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    Staff Emeritus
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    What voko said is exactly right. To elaborate, these two apparently different integrals differ only by a constant.
     
  5. Aug 5, 2013 #4
    So if I was to find the indefinite integral, both answers were right?
     
  6. Aug 5, 2013 #5
    None is correct unless you add the indefinite constant.
     
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