单词	line integral
释义	line integral If a vector function V (x,y,z) is defined between two points A and B on a curve, the curve is approximately given by a series of equal directed chords Δ1=,Δ2=,…Δn,= . In each segment i of the curve it is possible to define the scalar product Vi• Δil. If the sum of the scalar products is considered, the line integral is defined by An example of a line integral is given by the case of a force F acting on a particle in the field of the force. The line integral ?ABF•d= is the work done on the particle as it moves from A to B because of the force. If the line integral is taken round a closed path (loop), the line integral is denoted by ?CV•d= or ∮V•dl . A line integral for a scalar function φ(x,y,z) is defined in a similar way and is denoted ?ABφdl . It is also possible to define another type of line integral for a vector function V by ?ABV×dl
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