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Student[MultivariateCalculus][FunctionAverage] - return the average value of a function defined over a region
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Calling Sequence
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FunctionAverage(f(x), x=a..b, opts)
FunctionAverage(f(x,y), x=a..b, y=c..d, opts)
FunctionAverage(f(x,y,z), x=a..b, y=c..d, z=e..f, opts)
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Parameters
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f(x), f(x, y), f(x, y, z)
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algebraic expressions
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x, y, z
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name; independent variables
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a, b, c, d, e, f
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algebraic; limits of integration
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opts
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(optional) equation(s) of the form option=value where option is coordinates or output; specify output options
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Description
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The FunctionAverage command returns the average value of a function over a region in one-, two-, or three-dimensional space.
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The opts argument can contain any of the following equations that set output options.
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coordinates = cartesian[x,y], polar[r,theta] (2-D), cartesian[x,y,z], cylindrical[r,theta,z], or spherical[r,phi,theta]
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Determines the coordinate system being used. The first variable of polar, cylindrical, and spherical is assumed to be the radial component. The default is cartesian.
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output = value or integral
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This option controls the return value of the function.
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* output = value specifies that the average value of the function is returned. The default is output = value.
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* output = integral specifies that the inert form of the function average is returned.
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Examples
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![with(Student[MultivariateCalculus])](/support/helpjp/helpview.aspx?si=4251/file05044/math157.png)
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![FunctionAverage(r^2, r = 0 .. 1, t = 0 .. (1/2)*Pi, coordinates = polar[r, t])](/support/helpjp/helpview.aspx?si=4251/file05044/math175.png)
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