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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.2012-03-04
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    can you do this by hand, or use Matlab program? Thanks2012-03-04
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    Or the free alternative, GNU Octave: http://www.gnu.org/software/octave/2012-03-04
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    Have you read the [wikipedia page](http://en.wikipedia.org/wiki/Adaptive_quadrature)? Adaptive quadrature is very boring to do by hand. The [Adaptive Simpson's method](http://en.wikipedia.org/wiki/Adaptive_Simpson%27s_method) is easy to implement.2012-04-03

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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?2012-03-05
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    @JamesR - read the help page.2012-06-10
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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.