Mathematics

Example: Computing the Length of a Curve

You can use quad or quadl to compute the length of a curve. Consider the curve parameterized by the equations

where .

A three-dimensional plot of this curve is

• 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

The function hcurve computes the integrand

• function f = hcurve(t)
  f = sqrt(4*cos(2*t).^2 + sin(t).^2 + 1);
  

Integrate this function with a call to quad

• len = quad(@hcurve,0,3*pi)
  
  len =
     1.7222e+01
  

The length of this curve is about 17.2.

Numerical Integration (Quadrature)

Example: Double Integration