DLMF:1.6.E44 (Q225)

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DLMF:1.6.E44
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    Statements

    Defining formula
    ∬ S ( ∂ ⁡ F 2 ∂ ⁡ x - ∂ ⁡ F 1 ∂ ⁡ y ) ⁢ d A = ∫ C 𝐅 ⋅ d 𝐬 = ∫ C F 1 ⁢ d x + F 2 ⁢ d y . subscript double-integral 𝑆 partial-derivative subscript 𝐹 2 𝑥 partial-derivative subscript 𝐹 1 𝑦 𝐴 subscript 𝐶 ⋅ 𝐅 𝐬 subscript 𝐶 subscript 𝐹 1 𝑥 subscript 𝐹 2 𝑦 {\displaystyle{\displaystyle\iint_{S}\left(\frac{\partial F_{2}}{\partial x}-% \frac{\partial F_{1}}{\partial y}\right)\mathrm{d}A=\int_{C}\mathbf{F}\cdot% \mathrm{d}\mathbf{s}=\int_{C}F_{1}\mathrm{d}x+F_{2}\mathrm{d}y.}}
    0 references
    DLMF id
    DLMF:1.6.E44
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
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    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4addec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2addec
    0 references
     
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