DLMF:1.6.E53 (Q234): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: area of a parameterized smooth surface $$S$$ (locally) / rank
 
Normal rank
Property / Symbols used: area of a parameterized smooth surface $$S$$ (locally) / qualifier
 
test:

A ⁢ ( S ) 𝐴 𝑆 {\displaystyle{\displaystyle A(S)}}

A(S)
Property / Symbols used: area of a parameterized smooth surface $$S$$ (locally) / qualifier
 
xml-id: C1.S6.XMD15.m1cdec

Latest revision as of 15:01, 1 January 2020

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DLMF:1.6.E53
No description defined

    Statements

    test
    A ⁢ ( S ) = 2 ⁢ π ⁢ ∫ a b | x | ⁢ 1 + ( f ′ ⁢ ( x ) ) 2 ⁢ d x . 𝐴 𝑆 2 𝜋 subscript superscript 𝑏 𝑎 𝑥 1 superscript superscript 𝑓 ′ 𝑥 2 𝑥 {\displaystyle{\displaystyle A(S)=2\pi\int^{b}_{a}|x|\sqrt{1+(f^{\prime}(x))^{% 2}}\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:1.6.E53
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
    0 references
    Q10799
    test
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C1.S6.XMD12.m1cdec
    0 references
    area of a parameterized smooth surface $$S$$ (locally)
    test
    A ⁢ ( S ) 𝐴 𝑆 {\displaystyle{\displaystyle A(S)}}
    xml-id
    C1.S6.XMD15.m1cdec
    0 references
     
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