MATLAB Mathematics - SERC - Index of

Numerical Integration (Quadrature)
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
quadl
quadv
dblquad
triplequad
Use adaptive Simpson quadrature
Use adaptive Lobatto quadrature
Vectorized quadrature
Numerically evaluate double integral
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
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
xt () = sin( 2t)
, yt () = cos( t)
, zt () = t
where t ∈ [ 0,
3π]
.
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