DLMF:1.6.E54 (Q235)

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DLMF:1.6.E54
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    Statements

    Defining formula
    ∬ S f ⁢ ( x , y , z ) ⁢ d S = ∬ D f ⁢ ( 𝚽 ⁢ ( u , v ) ) ⁢ ∥ 𝐓 u × 𝐓 v ∥ ⁢ d u ⁢ d v . subscript double-integral 𝑆 𝑓 𝑥 𝑦 𝑧 𝑆 subscript double-integral 𝐷 𝑓 𝚽 𝑢 𝑣 norm subscript 𝐓 𝑢 subscript 𝐓 𝑣 𝑢 𝑣 {\displaystyle{\displaystyle\iint_{S}f(x,y,z)\mathrm{d}S=\iint_{D}f(% \boldsymbol{{\Phi}}(u,v))\|\mathbf{T}_{u}\times\mathbf{T}_{v}\|\mathrm{d}u% \mathrm{d}v.}}
    0 references
    DLMF id
    DLMF:1.6.E54
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    Q10799
    Defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C1.S6.XMD12.m1ddec
    0 references
     
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