Integration to Find Arc Length
This example shows how to parametrize a curve
and compute the arc length using
Consider the curve parameterized by the equations
x(t) = sin(2t), y(t) = cos(t), z(t) = t,
where t ∊ [0,3π].
Create a three-dimensional plot of this curve.
t = 0:0.1:3*pi; plot3(sin(2*t),cos(t),t)
The arc length formula says the length of the curve is the integral of the norm of the derivatives of the parameterized equations.
Define the integrand as an anonymous function.
f = @(t) sqrt(4*cos(2*t).^2 + sin(t).^2 + 1);
Integrate this function with a call to
len = integral(f,0,3*pi)
len = 17.2220
The length of this curve is about