DLMF:1.6.E51 (Q232)

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DLMF:1.6.E51
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    Statements

    test
    A ⁢ ( S ) = ∬ D 1 + ( ∂ ⁡ f ∂ ⁡ x ) 2 + ( ∂ ⁡ f ∂ ⁡ y ) 2 ⁢ d A . 𝐴 𝑆 subscript double-integral 𝐷 1 superscript partial-derivative 𝑓 𝑥 2 superscript partial-derivative 𝑓 𝑦 2 𝐴 {\displaystyle{\displaystyle A(S)=\iint_{D}\sqrt{1+\left(\frac{\partial f}{% \partial x}\right)^{2}+\left(\frac{\partial f}{\partial y}\right)^{2}}\mathrm{% d}A.}}
    0 references
    DLMF id
    DLMF:1.6.E51
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    test
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4ahdec
    0 references
     
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