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Student[Calculus1]

  

FunctionAverage

  

find the average value of a function or expression

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

FunctionAverage(f(x), x = a..b, opts)

FunctionAverage(f(x), a..b, opts)

Parameters

f(x)

-

algebraic expression in variable 'x'

x

-

name; specify the independent variable

a, b

-

algebraic expressions; specify the end points of the curve

opts

-

equation(s) of the form option=value where option is one of averageoptions, functionoptions, output, showaverage, showfunction, or Student plot options; specify output options

Description

• 

The FunctionAverage(f(x), x=a..b) command returns the average value of the expression fx on the interval from a to b. By using options, you can specify that the command returns a plot or inert integral instead.

• 

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

• 

The average value of an expression f(x) from x = a to x = b is the value of the expression:

∫abfxⅆxba

• 

The opts argument can contain any of the Student plot options or any of the following equations that (excluding output) set plot options.

  

 

  

averageoptions = list

  

A list of options for the plot of the average value of fx. By default, the average is plotted as a solid blue line. For more information on plot options, see plot/options.

  

 

  

functionoptions = list

  

A list of options for the plot of the expression fx.  By default, the expression is plotted as a solid red line. For more information on plot options, see plot/options.

  

 

  

output = value, integral, or plot

  

This option controls the return value of the function.

– 

output = value specifies that the average value is returned. Other options are ignored if output = value.  This is the default.

– 

output = integral specifies that the expression 1ba times the inert integral with the integrand f(x) is returned. Other options are ignored if output = integral.

– 

output = plot specifies that a plot, which shows the expression and its average value from a to b, is displayed.

  

 

  

showaverage = true or false

  

Whether the average of the expression fx over the range a..b is plotted. By default, the value is true.

  

 

  

showfunction = true or false

  

Whether the expression fx is plotted.  By default, the value is true.

  

 

  

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[Calculus1]:

FunctionAveragex3,x=1..1

3

(1)

FunctionAveragelnx,x=1..4

1+83ln2

(2)

FunctionAveragex32,1..4,output=integral

13∫14x3/2ⅆx

(3)

FunctionAverage1x,x=1..4,output=plot

FunctionAveragesinx+x,3..10,output=plot,functionoptions=thickness=2,averageoptions=linestyle=dash

See Also

int

plot/options

plot/typesetting

Student

Student plot options

Student[Calculus1]

Student[Calculus1][FunctionAverageTutor]

Student[Calculus1][VisualizationOverview]

 


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