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Math Help - Trig Integration help

  1. #1
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    Trig Integration help

    So I've hit a wall, and as with other times I've posted, I'm really only looking for the "kick-off" step for this problem: \int sin^2 x cos^2 x dx I have tried using the fact that the integrand is really a half-angle in disguise, but that leads to: \int (1/2) sin^2 x dx which seems more complicated than the original problem. I've also tried to replace either the sin or cos term with 1+ cos^2 x etc., but that quickly makes the problem more complicated, or lands me back at square one. Thanks in advance for any and all help.
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    Quote Originally Posted by flabbergastedman View Post
    So I've hit a wall, and as with other times I've posted, I'm really only looking for the "kick-off" step for this problem: \int sin^2 x cos^2 x dx I have tried using the fact that the integrand is really a half-angle in disguise, but that leads to: \int (1/2) sin^2 x dx which seems more complicated than the original problem. I've also tried to replace either the sin or cos term with 1+ cos^2 x etc., but that quickly makes the problem more complicated, or lands me back at square one. Thanks in advance for any and all help.
    note the power reduction identity ... \sin^2(u) = \frac{1-\cos(2u)}{2}

    \sin^2{x}\cos^2{x} = \frac{1}{4}\sin^2(2x) = \frac{1 - \cos(4x)}{8}
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    And that's the missing ingredient! Thank you very much
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