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Math Help - Help with double integral

  1. #1
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    Help with double integral

    Double integral of R (x(sin(x+y), R= [0,pi/6] X [0,pi/3]

    Thanks in advance.
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  2. #2
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    \begin{aligned}\int_0^{\pi/6}\int_0^{\pi/3}x\sin(x+y)\,dydx &= \int_0^{\pi/6}\Bigl[-x\cos(x+y)\Bigr]_0^{\pi/3}dx \\ &= \int_0^{\pi/6}\bigl(x\cos x-x\cos(x+\tfrac\pi3)\bigr)dx.\end{aligned}

    Now you have a single integral that you can integrate by parts.
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