line integral

noun

Mathematics.

1. the limit, as the norm of the partition of a given curve approaches zero, of the sum of the product of the length of the arcs in the partition times the value of the function at some point on each arc.

Word History and Origins

Origin of line integral¹

First recorded in 1870–75

Example Sentences

It is now well known as Stokes's theorem connecting a certain surface integral with a line integral, and has many applications both in physics and in geometry.

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The work done in carrying a unit magnetic pole once round a circuit conveying a current is called the “line integral of magnetic force” along that path.

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If, for instance, we carry a unit pole in a circular path of radius r once round an infinitely long straight filamentary current I, the line integral is 4πI.

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It is easy to prove that this is a general law, and that if we have any currents flowing in a conductor the line integral of magnetic force taken once round a path linked with the current circuit is 4π times the total current flowing through the circuit.

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If it is made endless, the magnetic force H is the same everywhere along the central axis and the line integral along the axis is Hl.

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