find the average value of a function or expression - Maple Help

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Student[Calculus1][FunctionAverage] - find the average value of a function or expression

Calling Sequence

FunctionAverage(f(x), x = a..b, opts)

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




algebraic expression in variable 'x'



name; specify the independent variable

a, b


algebraic expressions; specify the end points of the curve



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



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:



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.














See Also

int, plot/options, plot/typesetting, Student, Student plot options, Student[Calculus1], Student[Calculus1][FunctionAverageTutor], Student[Calculus1][VisualizationOverview]

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