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Cosine of 2 times theta

  1. Jun 17, 2011 #1
    1. The problem statement, all variables and given/known data

    From angles pi minus theta1 to pi plus theta1, what is the integral of cosine of 2 theta times d theta?

    2. Relevant equations



    3. The attempt at a solution

    When I evaluate this definite integral from pi minus theta1 to pi plus theta1, I get positive one half sine of 2 theta1.
    It should be NEGATIVE one half sine of 2 theta1.

    Is 2pi + 2theta1 and 2pi - 2theta1 somehow wrong????
     
  2. jcsd
  3. Jun 18, 2011 #2

    tiny-tim

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    Science Advisor
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    Hi PieOperator! :smile:

    (have a pi: π and a theta: θ and an integral: ∫ and try using the X2 tag just above the Reply box :wink:)

    you should have got [1/2 sin2θ]π-θ1π+θ1

    what happened then? :confused:
     
  4. Jun 18, 2011 #3
    Thanks. I found my mistake. It has to do with vectors and the correct orientation. It is positive one half sine of 2 theta in the incorrect vector orientation. I just have to reverse the direction of the vector, and the interval reverses as well.
     
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