Is there any other options of calculating integral instead of using quadratures? I know that also we can calculate spline function or use monte-carlo method but do you know something else?
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2$\begingroup$ isn't scicomp.stackexchange.com a better place for this question? $\endgroup$– Anton TrunovCommented Dec 25, 2015 at 12:44
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$\begingroup$ Computing an integral is quadrature... $\endgroup$– vonbrandCommented Dec 25, 2015 at 15:50
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$\begingroup$ @vonbrand. The Riemann integral is defined by a quadrature, but that doesn't necessarily preclude the existence of an algorithm that computes one without quadratures (though I'm not aware of any). $\endgroup$– Rick DeckerCommented Mar 2, 2016 at 0:07
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Another approach is to use a computer algebra to compute the integral exactly, symbolically.
See also Wikipedia's article on symbolic integration. Wikipedia also has a list of techniques and computational methods for integration.
