Mathematics

Numerical Integration (Quadrature)

The area beneath a section of a function F(x) can be determined by numerically integrating F(x), a process referred to as quadrature. The MATLAB quadrature functions are:

quad	Use adaptive Simpson quadrature
quadl	Use adaptive Lobatto quadrature
dblquad	Numerically evaluate double integral
triplequad	Numerically evaluate triple integral

To integrate the function defined by humps.m from 0 to 1, use

• q = quad(@humps,0,1)
  
  q =
      29.8583
  

Both quad and quadl operate recursively. If either method detects a possible singularity, it prints a warning.

You can include a fourth argument for quad or quadl that specifies a relative error tolerance for the integration. If a nonzero fifth argument is passed to quad or quadl, the function evaluations are traced.

Two examples illustrate use of these functions:

• Computing the length of a curve
• Double integration

Converting Your Optimization Code to MATLAB Version 5 Syntax

Example: Computing the Length of a Curve