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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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    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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    @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.