DLMF:1.6.E52 (Q204): Difference between revisions

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Latest revision as of 00:48, 3 March 2024

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DLMF:1.6.E52
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    Statements

    DLMF defining formula
    A ⁢ ( S ) = 2 ⁢ π ⁢ ∫ a b | f ⁢ ( x ) | ⁢ 1 + ( f ′ ⁢ ( x ) ) 2 ⁢ d x , 𝐴 𝑆 2 𝜋 subscript superscript 𝑏 𝑎 𝑓 𝑥 1 superscript superscript 𝑓 ′ 𝑥 2 𝑥 {\displaystyle{\displaystyle A(S)=2\pi\int^{b}_{a}|f(x)|\sqrt{1+(f^{\prime}(x)% )^{2}}\mathrm{d}x,}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    parameterized surface
    DLMF defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C1.S6.XMD12.m1bdec
    0 references
    area of a parameterized smooth surface $$S$$ (locally)
    DLMF defining formula
    A ⁢ ( S ) 𝐴 𝑆 {\displaystyle{\displaystyle A(S)}}
    xml-id
    C1.S6.XMD15.m1bdec
    0 references

    Identifiers

     
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