Antiderivative Plot - Maple Help

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 $f\left(x\right)$. 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 $f\left(x\right)$. 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 $f\left(x\right)$.  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 $f\left(x\right)$ 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 $f\left(x\right)$, is plotted.  By default, the value is false.
 showfunction = true or false
 Whether the expression $f\left(x\right)$ 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 $\left[a,b\right]$ specify that $b=F\left(a\right)+c$ for some constant $c$, where $F\left(x\right)$ is an antiderivative of f(x). The primary antiderivative is $F\left(x\right)+c$.
 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

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right):$
 > $f≔x↦3\cdot {x}^{2}-x$
 ${f}{≔}{x}{↦}{3}{\cdot }{{x}}^{{2}}{-}{x}$ (1)
 > $\mathrm{int}\left(f\left(x\right),x\right)$
 ${{x}}^{{3}}{-}\frac{{1}}{{2}}{}{{x}}^{{2}}$ (2)
 > $\mathrm{AntiderivativePlot}\left(f\left(x\right),\mathrm{output}=\mathrm{antiderivative}\right)$
 ${{x}}^{{3}}{+}{1050}{-}\frac{{1}}{{2}}{}{{x}}^{{2}}$ (3)
 > $\mathrm{AntiderivativePlot}\left(f\left(x\right),x=0..1,\mathrm{output}=\mathrm{antiderivative}\right)$
 ${{x}}^{{3}}{-}\frac{{1}}{{2}}{}{{x}}^{{2}}$ (4)
 > $\mathrm{AntiderivativePlot}\left(f\left(x\right),\mathrm{output}=\mathrm{antiderivative},\mathrm{value}=\left[0,0\right]\right)$
 ${{x}}^{{3}}{-}\frac{{1}}{{2}}{}{{x}}^{{2}}$ (5)
 > $\mathrm{AntiderivativePlot}\left(f\left(x\right),x=-1..1,\mathrm{value}=0\right)$
 > $\mathrm{AntiderivativePlot}\left(f\left(x\right),x=-1..1,\mathrm{value}=\left[0,1\right]\right)$
 > $\mathrm{AntiderivativePlot}\left(\mathrm{exp}\left(x\right)+x,x=0..3,\mathrm{showclass},\mathrm{showantiderivative}=\mathrm{false},\mathrm{functionoptions}=\left[\mathrm{thickness}=2\right],\mathrm{classoptions}=\left[\mathrm{color}=\mathrm{black}\right]\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{AntiderivativePlot}\left(f\left(x\right),-1..1,\mathrm{value}=0,\mathrm{showclass}\right)$