return the average value of a function defined over a region - Maple Help

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Student[MultivariateCalculus][FunctionAverage] - return the average value of a function defined over a region

Calling Sequence

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)

Parameters

f(x), f(x, y), f(x, y, z)

-

algebraic expressions

x, y, z

-

name; independent variables

a, b, c, d, e, f

-

algebraic; limits of integration

opts

-

(optional) equation(s) of the form option=value where option is coordinates or output; specify output options

Description

• 

The FunctionAverage command returns the average value of a function over a region in one-, two-, or three-dimensional space.

• 

The opts argument can contain any of the following equations that set output options.

  

 

  

coordinates = cartesian[x,y], polar[r,theta] (2-D), cartesian[x,y,z], cylindrical[r,theta,z], or spherical[r,phi,theta]

  

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.

  

 

  

output = value or integral

  

This option controls the return value of the function.

  

* output = value specifies that the average value of the function is returned. The default is output = value.

  

* output = integral specifies that the inert form of the function average is returned.

Examples

withStudent[MultivariateCalculus]:

FunctionAveragex3,x=3..4

1754

(1)

FunctionAveragex2+y2,y=0..1x2,x=0..1

12

(2)

FunctionAverager2,r=0..1,t=0..π2,coordinates=polarr,t

12

(3)

FunctionAveragex2+y2+z,z=2..4+y2,y=x1..x+6,x=2..4,output=integral

∫24∫x1x+6∫2y2+4x2+y2+zⅆzⅆyⅆx∫24∫x1x+6∫2y2+41ⅆzⅆyⅆx

(4)

FunctionAveragex2+y2,y=x2+4..x3,x=a..b

643b+643a130a10+130b10+121a7121b716a6+16b6+a5b5+203a3203b314a4+14b4+13a313b34b+4a

(5)

FunctionAveragex2+y2,y=x2+4..x3,x=0..4

218656175

(6)

FunctionAveragex2+y2,y=x2+4..x3,x=3..5

167391585005

(7)

See Also

Student, Student[MultivariateCalculus]


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