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Math Help - Double integral and wrong answer

  1. #1
    Member
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    Double integral and wrong answer

    As you see from the picture I got 8*pi. Book gives me 4*pi.
    Is my answer wrong or right?
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
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    802
    Hi

    \int_0^{2\pi}\mathrm{d}\varphi\int_0^2(1-2\rho \cos \varphi-3\rho \sin \varphi)\rho\,\mathrm{d}\rho=\int_0^{2\pi} \left[\frac{\rho^2}{\color{red}2}-2\frac{\rho^3}{3} \cos \varphi-3\frac{\rho^3}{3} \sin \varphi \right]_0^2\mathrm{d}\varphi

    and the result is 4\pi.
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