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Thread: Integral Question

  1. #1
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    Integral Question

    Hi

    Can someone tell me why this is incorrect.

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

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

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

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

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

    $\displaystyle u=cos(2x)$
    $\displaystyle du=-sin(2x)$

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

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

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

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

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