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- Q467699 subject Q6103418.
- Q467699 subject Q8811519.
- Q467699 abstract "In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour integral as well, although that is typically reserved for line integrals in the complex plane.The function to be integrated may be a scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes the line integral from simpler integrals defined on intervals. Many simple formulae in physics (for example, W = F · s) have natural continuous analogs in terms of line integrals (W = ∫C F · ds). The line integral finds the work done on an object moving through an electric or gravitational field, for example.".
- Q467699 thumbnail Line_integral_of_scalar_field.gif?width=300.
- Q467699 wikiPageExternalLink ContourIntegralMod.html.
- Q467699 wikiPageExternalLink line_integral_vector_field_introduction.
- Q467699 wikiPageExternalLink introduction-to-the-line-integral?playlist=Calculus.
- Q467699 wikiPageExternalLink line-integral-example-1?playlist=Calculus.
- Q467699 wikiPageExternalLink line-integral-example-2--part-1?playlist=Calculus.
- Q467699 wikiPageExternalLink line-integral-example-2--part-2?playlist=Calculus.
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- Q467699 comment "In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour integral as well, although that is typically reserved for line integrals in the complex plane.The function to be integrated may be a scalar field or a vector field.".
- Q467699 label "Line integral".
- Q467699 depiction Line_integral_of_scalar_field.gif.