6.19.2 Length of an arc: arcLen
The arcLen command finds the lengths of curves in the plane,
which can either be given by an equation or a curve object.
To find the length of a curve given by an equation:
-
arcLen takes four arguments:
-
expr, an expression (resp. a list of two expressions [expr1,expr2])
involving a variable x.
- x, the name of the variable.
- a and b, two values for the bounds of this variable.
- arcLen(expr,x,a,b)
(resp.
arcLen([expr1,expr2]x,a,b))
returns the length of the curve defined by
y=f(x)=expr (resp. by
x1=expr1,x2=expr2) as x varies from
a to b, using the formula
or
Examples.
-
Compute the length of the parabola y=x2 from x=0 to x=1.
Input:
arcLen(x^2,x,0,1)
or:
arcLen([t,t^2],t,0,1)
Output:
- Compute the length of the curve y=cosh(x) from x=0 to
x=ln(2).
Input:
arcLen(cosh(x),x,0,log(2))
Output:
- Compute the length of the circle x=cos(t),y=sin(t) from t=0 to
t=2*π.
Input:
arcLen([cos(t),sin(t)],t,0,2*pi)
Output:
To find the length of a curve given by a curve object:
-
arcLen takes a single argument: curve, a
geometric curve defined in one of the graphics chapters (chapters
13 and 14).
- arcLen(curve) returns the length of the
curve.
Examples.