Numerical Integration - Numerical Methods in Engineering with MATLAB - page 250

MATLAB Functions

I = quad(func,a,b,tol) uses adaptive Simpson's rule =

a f ( x ) dx with an error tolerance tol (default is 1.0e-6). To speedupexecution,
vectorize the computation of func by using array operators .*, ./ and .ˆ in the
definition of func .For example, if f ( x )

for evaluating I

x 3 sin x = + 1 / x ,specify the functionas

function y = func(x)
y = (x.ˆ3).*sin(x) + 1./x

I = dblquad(func,xMin,xMax,yMin,yMax,tol) uses quad to integrate overa
rectangle:

yMax xMax

I = f ( x , y ) dx dy

yMin xMin

I = quadl(func,a,b,tol) employs adaptive Lobatto quadrature (this methodis
not discussedinthis topic). It is recommendedif very high accuracyis desired
and the integrand issmooth.

There are nofunctionsfor Gaussian quadrature.