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
quadv	Vectorized 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

Troubleshooting

Example: Computing the Length of a Curve

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