DLMF:1.6.E53 (Q234)

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DLMF:1.6.E53
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    Statements

    Defining formula
    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
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
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