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
^
2,x,0,1)^
2],t,0,1)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:
Output:
Input:
Output: