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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=2=,…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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更新时间:2025/6/23 5:33:59