# Adaptive Quadrature

How can we use adaptive quadrature to approximate the following integral to $10^{-5}$?

$$\int_0^{\pi/2}(6\cos4x+4\sin6x)e^x\,dx$$

Thanks

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Do you want an algorithm, or want someone to point you to a software package that you can use to actually compute it? In the event of the latter, what's your favorite language? I can suggest solutions in C/C++, Matlab, and Python. – Jerry Gagelman Mar 4 '12 at 14:08
can you do this by hand, or use Matlab program? Thanks – James R. Mar 4 '12 at 19:06
Or the free alternative, GNU Octave: gnu.org/software/octave – dls Mar 4 '12 at 19:40
Have you read the wikipedia page? Adaptive quadrature is very boring to do by hand. The Adaptive Simpson's method is easy to implement. – lhf Apr 3 '12 at 20:00

## 2 Answers

Gander and Gautschi present MATLAB code for two different adaptive quadrature methods. One is based on Simpson's rule, while the other is based on the Gauss-Lobatto rule with a Kronrod extension (a modification of the usual Gaussian quadrature method). It should be straightforward to modify the code given in that paper to have it evaluate your integral.

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If you have access to Matlab, just use the quadl function: http://www.mathworks.com/help/techdoc/ref/quad.html

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can you put modify the matlab code for the function of interest in this question? – James R. Mar 5 '12 at 8:13
@JamesR - read the help page. – nbubis Jun 10 '12 at 6:54