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Line integral - Wikipedia

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In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.[1] The terms path integral, curve integral, and curvilinear integral are also used; contour integral is used 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, such as the definition of work as 𝑊 = 𝐹 ⋅ 𝑠 , have natural continuous analogues in terms of line integrals, in this case 𝑊 = ∫ 𝐿 𝐹 ( 𝑠 ) ⋅ 𝑑 𝑠 , which computes the work done on an object moving through an electric or gravi

Line integral - Wikipedia Jump to content From Wikipedia, the free encyclopedia Definite integral of a scalar or vector field along a path This article needs more citations . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . Find sources: "Line integral" – news · newspapers · books · scholar · JSTOR ( June 2023 ) ( Learn how and when to remove this message ) Part of a series of articles about Calculus ∫ a b f ′ ( t ) d t = f ( b ) − f ( a ) {\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)} Fundamental theorem Limits Con

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