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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 = [DEFAULTor numeric..numeric, DEFAULTor 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 .

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right)\:$

$f≔x\mapsto 3\cdot x^2-x$

$f≔x\mapsto 3\cdot x^2-x$

$\mathrm{int}\left(f\left(x\right)\,x\right)$

$x^3-\frac{1}{2}{x}^2$

$\mathrm{AntiderivativePlot}\left(f\left(x\right)\,\mathrm{output}=\mathrm{antiderivative}\right)$

$x^3+1050-\frac{1}{2}{x}^2$

$\mathrm{AntiderivativePlot}\left(f\left(x\right)\,x=0..1\,\mathrm{output}=\mathrm{antiderivative}\right)$

$x^3-\frac{1}{2}{x}^2$

$\mathrm{AntiderivativePlot}\left(f\left(x\right)\,\mathrm{output}=\mathrm{antiderivative}\,\mathrm{value}=\left[0\,0\right]\right)$

$x^3-\frac{1}{2}{x}^2$

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

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

$\mathrm{AntiderivativePlot}\left(\exp \left(x\right)+x\,x=0..3\,\mathrm{showclass}\,\mathrm{showantiderivative}=\mathrm{false}\,\mathrm{functionoptions}=\left[\mathrm{thickness}=2\right]\,\mathrm{classoptions}=\left[\mathrm{color}=\mathrm{black}\right]\right)$

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