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Math Help - Vector Calculus (area)

  1. #1
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    Vector Calculus (area)

    Calculate \iint\limits_S \vec{F} .\vec{n} dS :

    \vec{F}(x,y,z) = (x,y 2x - x - y)

    S: x^{2} + y^{2} - z^{2} = 0, \ 1 \leq z \leq 4 and x^2 + y^2 = 1, \ 0 \leq z \leq 1


    Answer.: -40pi
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Vector Calculus (area)

    Hint: Decompose the integral as \iint_{S_1}F\cdot n\;dS+\iint_{S_2}F\cdot n\;dS with S_1:x^2+y^2-z^2=0,\;1\leq z \leq 4 and S_2:x^2+y^2=1,\;0\leq z \leq 1 .
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  3. #3
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    Re: Vector Calculus (area)

    Thanks very much. I'll try to solve it in this way.
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