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Math Help - Integrating expression by power reduction formula

  1. #1
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    Smile Integrating expression by power reduction formula

    Hi everyone! So, I have to integrate the expression:

    sin2(x/2) dx

    in the book it says that it integrates to become:

    1/2 - cosx / 2

    In order to get there, the power reduction formula is used, I am just not sure how to use the formula when the initial expression is not sin2x?

    Thanks for reading
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  2. #2
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    Re: Integrating expression by power reduction formula

    The power-reducing formula,
    sin2 u = (1 - cos 2u)/2,
    can be used in cases other than u = x.

    Here you need to replace u, in each instance, with x/2.

    This results in the relevant formula to your case,

    sin2 x/2 = (1 - cos 2(x/2))/2 or
    sin2 x/2 = (1 - cos x)/2.

    Hope this helps.
    Thanks from Nora314
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  3. #3
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    Re: Integrating expression by power reduction formula

    Thank you so much for the help! I understand completely now,
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