DLMF:1.5.E42 (Q169)

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DLMF:1.5.E42
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    Statements

    test
    ∬ D f ⁢ ( x , y ) ⁢ d x ⁢ d y = ∬ D * f ⁢ ( x ⁢ ( u , v ) , y ⁢ ( u , v ) ) ⁢ | ∂ ⁡ ( x , y ) ∂ ⁡ ( u , v ) | ⁢ d u ⁢ d v , subscript double-integral 𝐷 𝑓 𝑥 𝑦 𝑥 𝑦 subscript double-integral superscript 𝐷 𝑓 𝑥 𝑢 𝑣 𝑦 𝑢 𝑣 partial-derivative 𝑥 𝑦 𝑢 𝑣 𝑢 𝑣 {\displaystyle{\displaystyle\iint_{D}f(x,y)\mathrm{d}x\mathrm{d}y=\iint_{D^{*}% }f(x(u,v),y(u,v))\left|\frac{\partial(x,y)}{\partial(u,v)}\right|\mathrm{d}u% \mathrm{d}v,}}
    0 references
    DLMF id
    DLMF:1.5.E42
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    Q10777
    test
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6agdec
    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.m4avdec
    0 references
     
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