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5.19.2  Length of an arc : arcLen

arcLen takes four arguments : an expression ex (resp. a list of two expressions [ex1,ex2]), the name of a parameter and two values a and b of this parameter.
arcLen computes the length of the curve define by the equation y=f(x)=ex (resp. by x=ex1,y=ex2) when the parameter values varies from a to b, using the formula arcLen(f(x),x,a,b)=
integrate(sqrt(diff(f(x),x)^2+1),x,a,b)
or
integrate(sqrt(diff(x(t),t)^2+diff(y(t),t)^2),t,a,b).
Examples

Alternatively, the arcLen command can take a single argument of a geometric curve defined in one of the graphics chapters (chapters 12 and 13).
Input:

arcLen(circle(0,1,0,pi/2))

Output:

1/2*pi

Input:

arcLen(arc(0,1,pi/2))

Output:

sqrt(2)/4*pi

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