Student[VectorCalculus][SurfaceInt] - compute the surface integral of a function from R^3 to R
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Calling Sequence
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SurfaceInt(f, domain, output = output_type)
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Parameters
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f
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algebraic expression; specify the function to be integrated
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domain
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list(name) = surface; specify the list of variable names and the surface over which to integrate
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output = output_type
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(optional) equation; specify 'integral' or 'value' for output_type; specify 'integral' for the function to return an inert integral, and 'value' to return the computed output
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Description
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The SurfaceInt(f, domain) calling sequence computes the surface integral of the function over the surface specified on the right-hand side of domain. The left-hand side of domain is the list of variables of the function .
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If integral is specified for output_type, the command returns an unevaluated integral; if value is specified, the command returns the computed value of the integral. The default value for output_type is value.
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Specify the surface domain using unevaluated function calls. The possible surfaces are Box, Sphere, and Surface.
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Each must have type algebraic..algebraic. These represent the sides of the box. The surface integral is taken over each face of the box.
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The first parameter of Sphere, center, must have type 'Vector'(3, algebraic). The second parameter radius must have type algebraic. These represent the center and radius of the sphere, respectively. If a coordinate system attribute is specified on center, the center is interpreted in this coordinate system.
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Surface(v, range, coordinate_system)
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The first argument, , must have type 'Vector'(3, algebraic). The second argument, range, can be:
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* [name1, name2] = region(arguments) where region is any two-dimensional region that Student[VectorCalculus][int] accepts: Circle, Ellipse, Rectangle, Region, Sector, or Triangle.
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* name1=range1, name2=range2 This explicitly specifies the ranges for the two parameters.
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If the optional final argument, coordinate_system, is specified, it must be an equation of the form coords=nameri or coordinates=name, where name is a recognized coordinate system. is interpreted in the specified coordinate system.
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Examples
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