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I am trying to understand why the following function does not provide problems to being computed numerically:

∫dx1/(sin(abs(x)^(1/2))) from x=-1 to x=2.

Clearly there is a singularity for x=0 but why does taking the absolute value of x and then taking its square root solve the problem?

I searched for quite a while on the internet and on numerical integration books and was surprised that I couldn't find the answer for that. Apparentlly there is a lack of documentation on singularity removal techniques on the web or I am not searching with the right keywords.Any introductory documentation on the subject is welcome!

For the record I am using matlab built-in functions such as quadtx() or integral() to solve it but I that's not the point since it turns out even the most simple simpson rule algorithm can deal with that integral.

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# Numerical integration - Techniques to remove singularities

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