4, output = integralĪrcLength ⁡ cosh ⁡ x, x = 1. 10, coordinates = polarĪrcLength ⁡ x 3 2, x = 1. 2 ⁢ π, coordinates = polarĪrcLength ⁡ sqrt ⁡ x, ln ⁡ x, x = 1. − 2 + arctanh ⁡ 2 2 + 17 − arctanh ⁡ 17 17ĪrcLength ⁡ cos ⁡ x, sin ⁡ x, x = 0. For more information about specifying a caption, see plot/typesetting. caption = '' disables the default caption. The default caption is constructed from the parameters and the command options. Whether the cumulative arc length is plotted. Output = plot specifies that a plot, which shows the expression, integrand of the expression, and cumulative arc length of the expression from the point a, is displayed. Other options are ignored if output = integral. Output = integral specifies that an inert integral with the appropriate integrand is returned. Other options are ignored if output = value. Output = value specifies that the value of the arc length is returned. This option controls the return value of the function. For more information on plot options, see plot/options. By default, the integrand is plotted as a solid blue line. Ī list of options for the plot of the integrand. By default, the cumulative arc length is plotted as a solid green line. Ī list of options for the plot of the cumulative arc length of the expression f ⁡ x. By default, the expression is plotted as a solid red line. By default, the expressions are represented with cartesian coordinates.Ī list of options for the plot of the expression f ⁡ x. This option specifies whether cartesian or polar coordinates are used. The opts argument can contain any of the Student plot options or any of the following equations that (excluding coordinates and output ) set plot options. If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

Also, most closed form formulae contain special functions that are beyond the normal scope of a first course in single-variable calculus.

In general, a closed form formula for the arc length cannot be determined. By using options, you can specify that the command returns a plot or inert integral instead. The ArcLength(, x=a.b) command returns the parametric arc length expressed in cartesian coordinates. The ArcLength(f(x), x=a.b) command returns the arc length of the expression expression f ⁡ x from a to b. b, opts )Īlgebraic expressions specify the end points of the curveĮquation(s) of the form option=value where option is one of coordinates, functionoptions, integraloptions, integrandoptions, output, showfunction, showintegral, showintegrand, or Student plot options specify output options

Arc length formula calculus