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Math Help - Integral Question

  1. #1
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    Integral Question

    Hi

    Can someone tell me why this is incorrect.

    \int sin^2(x)cos^2(x)dx

    \int (0.5(1-cos(2x))(0.5(cos(2x)+1))dx

    \int (0.5-\frac{cos(2x)}{2})(\frac{cos(2x)}{2}+0.5))dx

    \int \frac{1}{4} - \frac{cos^2(x)}{4} dx

    \frac{1}{4} \int dx - \frac{1}{4} \int cos^2(2x)

    u=cos(2x)
    du=-sin(2x)

    \frac{x}{4} - \frac{1}{4} \int u^2 du

    \frac{x}{4} - \frac{1}{4} * \frac{u^3}{3} +c

    \frac{x}{4} - \frac{1}{4} * \frac{cos^3(2x)}{12} +c

    P.S
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  2. #2
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    For one thing, the substitution is incorrect. You have no \sin (2x) in the integral to get to u^2 du. You have also differentiated u incorrectly.
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  3. #3
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    Till the above step you are right.

    Next write cos^2(2x) = \frac{1}{2}(1+cos4x) and proceed.
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