line integral of a vector field (Q116784237)

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integral of a vector field along a path

• scalar line integral
• line integral

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Language	Label	Description	Also known as
English	line integral of a vector field	integral of a vector field along a path	scalar line integral line integral

Statements

subclass of

line integral

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defining formula

${\displaystyle \int _{\boldsymbol {c}}{\boldsymbol {F}}\cdot \mathrm {d} {\boldsymbol {s}}=\int _{a}^{b}{\boldsymbol {F}}({\boldsymbol {c}}(t))\cdot {\boldsymbol {c}}'(t)\,\mathrm {d} t}$

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in defining formula

${\displaystyle \int _{\boldsymbol {c}}{\boldsymbol {F}}\cdot \mathrm {d} {\boldsymbol {s}}}$

symbol represents

line integral of a vector field

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${\displaystyle {\boldsymbol {c}}}$

symbol represents

path

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${\displaystyle {\boldsymbol {F}}}$

symbol represents

vector field

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${\displaystyle \int _{a}^{b}f(x)\,\mathrm {d} x}$

symbol represents

definite integral

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${\displaystyle '}$

symbol represents

derivative

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${\displaystyle \cdot }$

symbol represents

scalar product

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maintained by WikiProject

WikiProject Mathematics

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different from

line integral of a scalar field

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Identifiers

Digital Library of Mathematical Functions ID

1.6.E38

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IEV number

102-05-04

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MathWorld ID

LineIntegral

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Sitelinks

Wikipedia(1 entry)

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• enwiki Line integral of a vector field

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