Line Integral
The line integral report is represented in the simulation tree by a node. Right-click this node to access the pop-up menu of the line integral report.
As a statistical report, the line integral largely has the same properties as the others of this type. However its Field Function property selects a scalar or vector field function value upon which the report is based.
A line integral refers to an integral of a function, whether it is a scalar or a vector field, along a curve. One example of using a line integral is calculating the amount of work done on a particle by a force field as it moves along an arbitrary curve in that vector field.
To compute a line integral, a parameterization of the curve is used, that is, is expressed by a vector function , with . Here, and are the initial and end point of the curve, respectively.
The line integral of a scalar field along a parametric curve is:
where is the distance between points on the curve.
The line integral of a vector field is:
where is the distance vector between points on the curve.
Reversing the orientation of curve does not change the value of the line integral of a scalar field but reverses the sign of the line integral of a vector field.
The following limitations exist when you work with vector quantities:
- The start and end points for the integration cannot be user-specified.
- The display does not indicate the direction of integration of the line.