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Thread: Stuck on simple integral

  1. #1
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    Stuck on simple integral

    Hey all, stuck on a simple integrand..

    $\displaystyle \int_0^\frac{\pi}{3} \! xcos(2x) \, \mathrm{d}x.$

    I get..

    $\displaystyle u = cos(2x) \; dv = xdx \; du = -2sin(2x) \; v = \frac{x^2}{x}$

    $\displaystyle \int xcos(2x) dx = uv - \int vdu \Rightarrow \frac{x^2}{x}cos(2x) - \int -x^2sin(2x) $

    Problem is the new integral isn't any easier to solve..
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  2. #2
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    You nearly always choose the polynomial function to be $\displaystyle \displaystyle u$, because differentiating reduces its power, and eventually becomes a constant...
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  3. #3
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    Do you know "ILATE" rule? According to that u should be x and dv should be cos(2x). Now try.
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  4. #4
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    Forgot about LATE. Thanks.
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