This section introduces various methods for estimating the integral of a function. Classical methods, such as the trapezoidal rule and Simpson's approximation, are mentioned but not recommened for general use. Methods, such as Romberg integration, which involve successive approximations are recommended. Improper integrals, in which the integrand is poorly behaved at the endpoints, need special treatment.
Gaussian quadrature is very efficient for dealing with special classes of integrands.
Multidimensional integration over a region with a simple boundary can be performed by repeated one dimensional integration. The exercise is an application of Gauss-Laguerre and Romberg integration. Numerical Recipies, chapter 4. By clicking the above thumbnail page images, you can peruse the slides. The entire set of slides for this course is available in colour postscript or in black and white postscript .