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Student[Calculus1][AntiderivativePlot] - find the antiderivative(s) of an expression

Calling Sequence

AntiderivativePlot(f(x), x, opts)

AntiderivativePlot(f(x), x = a..b, opts)

AntiderivativePlot(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 plot range

opts

-

plotting options or equation(s) of the form option=value where option is one of antiderivativeoptions, classoptions, functionoptions, output, showantiderivative, showclass, showfunction, value, or Student plot options; specify options for the plot

Description

• 

The AntiderivativePlot(f(x), x=a..b) command plots the expression and a primary antiderivative.

• 

As well as plotting one antiderivative, a class of antiderivatives can be viewed by using the showclass option.

• 

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

• 

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

  

 

  

antiderivativeoptions = list

  

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

  

 

  

classoptions = list

  

A list of options for the plot of a class of antiderivatives of the expression fx. By default, each antiderivative is plotted as a solid green 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 = antiderivative or plot

  

This option controls the return value of the function.

– 

output = antiderivative specifies that the primary antiderivative is returned. Other options are ignored if output = antiderivative (except value).

– 

output = plot specifies that the output should be a plot of the function and its antiderivative(s).  This is the default.

  

 

  

showantiderivative = true or false

  

Whether the primary antiderivative of fx is plotted.  By default, the value is true.

  

 

  

showclass = true or false

  

Whether a class of functions, each of which is a valid antiderivative of fx, is plotted.  By default, the value is false.

  

 

  

showfunction = true or false

  

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

  

 

  

value = algebraic, Vector or list

  

Determines the primary antiderivative. By default, the primary antiderivative plotted is the one whose value at the left end point is 0.

  

An algebraic value for this option specifies the value of the primary antiderivative at the left end point of the range.

  

A two-dimensional Vector or list with two values specifies the value of the primary antiderivative at a point. The second value specifies the value of the primary antiderivative evaluated at the first value. That is, a,b and a,b specify that b=Fa+c for some constant c, where Fx is an antiderivative of f(x). The primary antiderivative is Fx+c.

  

 

  

view = [DEFAULT or numeric..numeric, DEFAULT or numeric..numeric]

  

The view of the final plot.

  

 

  

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]:

f:=x→3x2x

f:=x→3x2x

(1)

∫fxⅆx

x312x2

(2)

AntiderivativePlotfx,output=antiderivative

x3+105012x2

(3)

AntiderivativePlotfx,x=0..1,output=antiderivative

x312x2

(4)

AntiderivativePlotfx,output=antiderivative,value=0,0

x312x2

(5)

AntiderivativePlotfx,x=1..1,value=0

AntiderivativePlotfx,x=1..1,value=0,1

AntiderivativePlotⅇx+x,x=0..3,showclass,showantiderivative=false,functionoptions=thickness=2,classoptions=color=black

The command to create the plot from the Plotting Guide is

AntiderivativePlotfx,1..1,value=0,showclass

See Also

plot/options, plot/typesetting, Student, Student plot options, Student[Calculus1], Student[Calculus1][AntiderivativeTutor], Student[Calculus1][VisualizationOverview]


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