In mathematics, a "'line integral "'is an integral where the differential vector in the curve ).
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Where is a line integral along the positively oriented if and only if forms a positively oriented basis for ( right-hand rule ).
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In contrast to the one-dimensional line integrals encountered in elementary physics, the contour of constant energy possesses a vast number of dimensions.
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If the parametrization \ gamma is continuously differentiable, the line integral can be evaluated as an integral of a function of a real variable:
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When a vector field represents force, the line integral of a vector field represents the curl ( which represents the rotation of a flow ).
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Holding that point fixed, the line integral over the path of the electric currents is calculated to find the total magnetic field at that point.
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Therefore generally the total attenuation p of a ray at position, on the projection at angle \ theta, is given by the line integral:
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Where the definition of the line integral is used in the first equality, and the fundamental theorem of calculus is used in the third equality.
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But I ran into problems when trying to derive it more generally by taking the line integral ( over the particle's path C ):
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The law is a physical example of a line integral, being evaluated over the path " C " in which the electric currents flow.
