In mathematics, a line integral (sometimes called a path integral or curve integral; not to be confused with calculating arc length using integration) is an integral where the function to be integrated is evaluated along a curve. Various different line integrals are in use. A specific case of an integration along a closed curve in two dimensions or the complex plane is the contour integral.
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 weighing distinguishes the line integral from simpler integrals defined on intervals. Many simple formulae in physics (for example, ) have natural continuous analogs in terms of line integrals (). The line integral finds the work done on an object moving through an electric or gravitational field, for example.
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Fri, 08 May 2009 15:30:18 GM
e: You guys want to talk about it from people language, I am trying to talk about it from dharma language. That's fine as far as it goes. I would add that there is no one dharma language appropriate to all. ...
