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Math Help - Integration by evaluation

  1. #1
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    Integration by evaluation

    I need some help with an integration question that's been bugging me. I just can't identify the conclusions applied to the following jump:

    integral of 1 - 0.5sin squared 2theta dtheta (between 0 and pi/2) = integral of 1 - 0.25(1 - cos4theta) dtheta (between 0 and pi/2)

    can anyone help?

    Thank you
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  2. #2
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    Quote Originally Posted by maggiec View Post
    I need some help with an integration question that's been bugging me. I just can't identify the conclusions applied to the following jump:

    integral of 1 - 0.5sin squared 2theta dtheta (between 0 and pi/2) = integral of 1 - 0.25(1 - cos4theta) dtheta (between 0 and pi/2)

    can anyone help?

    Thank you
    used the power reduction identity ...

    \sin^2{u} = \frac{1 - \cos(2u)}{2}
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  3. #3
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    Quote Originally Posted by skeeter View Post
    used the power reduction identity ...

    \sin^2{u} = \frac{1 - \cos(2u)}{2}
    Can I also ask, what is this identity a derivation of?
    Thanks
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  4. #4
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by maggiec View Post
    Can I also ask, what is this identity a derivation of?
    Thanks
    Double-Angle and Half-Angle Formulas
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