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

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1akdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aidec
Property / Symbols used
 
Property / Symbols used: Q10799 / rank
 
Normal rank
Property / Symbols used: Q10799 / qualifier
 
Defining formula:

S 𝑆 {\displaystyle{\displaystyle S}}

S
Property / Symbols used: Q10799 / qualifier
 
xml-id: C1.S6.XMD12.m1cdec
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
 
Defining formula:

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 16:01, 1 January 2020

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DLMF:1.6.E53
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    Statements

    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.}}
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    DLMF:1.6.E53
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1akdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aidec
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    S 𝑆 {\displaystyle{\displaystyle S}}
    C1.S6.XMD12.m1cdec
    0 references
    A ( S ) 𝐴 𝑆 {\displaystyle{\displaystyle A(S)}}
    C1.S6.XMD15.m1cdec
    0 references