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I am studying Gauss Legendre quadrature. I understand the concept and the specifics values that we need to use when applying the formula.

However I am trying to understand if it is possible to integrate a function using the Gauss Legendre method over a certain interval but with a specific step size h,( divided in intervals), as we can do when using another quadrature method.

Basically I am confusing because I cannot find any formula but I read somewhere that if we increase the N ( number of intervals) the result will be more accurate. So is there any Composite Gauss Legendre formula as we have for Composite Simpson method for example?

Thank you

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Just split the interval $I = [a,b]$ over which you want to integrate and apply a certain Gauss-Legendre formula over each subinterval. There is no such thing as a closed formula as in the case of Newton-Cotes.

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    Hi I do not understand. I know that I have to map the interval [a,b] to the interval [-1,1] and then apply the formula using the weights and the correspondent x nodes in the formula, but if for example I have the interval [1,5] and I want to split the interval in 5 (N=5) what should I do? I cannot find exercises to help me to understand this. Can you help on this? Or do you know any website that I can find more information? thanks – 2017-02-08
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    @user290335 You split your interval $[1,5]$ into for example $[1,3]$, $[3,4]$ and $[4,5]$ and then apply on each interval the Gauss-Legendre formula separately and add the results together. – 2017-02-08
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    So every time I subdivide the interval into [1,3],[3,4] etc. as you said I need to map that interval to the interval [-1,1] and use the new function that I need to integrate by mapping the intervals? And if I have N=200? will be the same or is there any other way? – 2017-02-09