compute the line integral of a vector field in R^2 or R^3 - Maple Help

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Student[VectorCalculus][LineInt] - compute the line integral of a vector field in R^2 or R^3

Calling Sequence

LineInt(F, dom, options)

Parameters

F

-

vector field or a Vector-valued procedure; specify the vector field to integrate

dom

-

unevaluated function call; specify the path of integration

options

-

(optional) equation(s) of the form option=value where option is one of output, fieldoptions, pathoptions, title, vectoroptions, or view

Description

• 

The LineInt(F, dom) calling sequence computes the line integral of the vector field F over the path specified by dom.

• 

Specify the path of integration using unevaluated function calls.  The possible paths of integration are Circle, Line, LineSegments, and Path.

  

Circle(center, radius)

  

The parameter center is the center of the circle and must have type 'Vector'(algebraic). The parameter radius is the radius of the circle and must have type algebraic.

  

Line(p1, p2)

  

The parameters p1 and p2 must have type 'Vector'(algebraic). They represent the endpoints of the directed line segment from p1 to p2.

  

LineSegments(p1, p2, ..., pk)

  

Similar to Line(p1, p2), the parameters pi represent the endpoints of k1 line segments.  The path of integration is the collection of line segments directed from p1 to p2, p2 to p3, ..., and p(k-1) to pk.

  

Path(v, range)

  

The first parameter, v, is a Vector representing the components of the path. The second parameter, range, must have type {range, name=range}.  If no parameter name is specified in range, it is inferred from v.

• 

The options arguments primarily control plot options.

  

output = value, plot, or integral

  

This option controls the return value of the command.

  

* output = value returns the value of the line integral. Plot options are ignored if output = value.  This is the default value.

  

* output = plot returns a plot of the path, tangent vectors of the path, and vector field.

  

* output = integral returns the inert representation of the line integral. Plot options are ignored if output = integral.

• 

fieldoptions = list

  

A list of plot options for plotting the Vector field. For more information on plotting options, see plot/options. The default value is [].

• 

pathoptions = list

  

A list of plot options for plotting the path. For more information on plotting options, see plot/options. The default value is [].

• 

title = string

  

Give the plot a title. The default value is the empty string.

• 

vectoroptions = list

  

A list of plot options for plotting the tangent vectors. For more information on plotting options, see plot/options. The default value is [].

• 

view = [realcons..realcons, realcons..realcons, realcons..realcons] (3-D) or [realcons..realcons, realcons..realcons] (2-D)

  

Specify the plot view. For more information, see plot3d/option or plot/options.

• 

caption = anything

  

A caption for the plot.

  

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption , see plot/typesetting.

Examples

withStudent[VectorCalculus]:

LineIntVectorFieldx,y,Line1,2,3,4

10

(1)

LineIntVectorFieldx,y,Line1,2,3,4,output=integral

∫0110+40tⅆt

(2)

LineIntVectorFieldx,y,LineSegments0,0,1,1,1,1

1

(3)

LineIntVectorFieldx2,y2,Patht,t2,t=0..2

24

(4)

LineIntVectorFieldy,x,z,Line0,0,0,1,1,1

12

(5)

The commands to create the plots from the Plotting Guide are

LineIntVectorFieldy,x,Circle0,0,1,output=plot,pathoptions=color=blue,vectoroptions=color=green,fieldoptions=color=red,scaling=constrained

LineIntVectorFieldy,x,z,Line0,0,0,1,1,1,output=plot,axes=boxed,orientation=170,85,5

See Also

plot/options, plot3d/option, realcons, Student[VectorCalculus], Student[VectorCalculus][Flux], Student[VectorCalculus][int], Student[VectorCalculus][PathInt], Student[VectorCalculus][SetCoordinates], Student[VectorCalculus][SurfaceInt], Student[VectorCalculus][Vector], Student[VectorCalculus][VectorField], VectorCalculus, VectorCalculus[LineInt]


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