This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

Integration to Find Arc Length

This example shows how to parametrize a curve and compute the arc length using integral.

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;

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 integral.

len = integral(f,0,3*pi)
len =

The length of this curve is about 17.2.

Was this topic helpful?