# symbolic integration

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R yan on 22 Jul 2011
Answered: John D'Errico on 9 Oct 2020
I am trying to find integral(definite) of f(x,y) with respect to x first and then with respect to y. I tried symbolic tools it works fine. But in case the integral of f w.r.to x could not be found, then can we do it using quadrature rule and then find integral wrt y.
thanks

Walter Roberson on 22 Jul 2011
Have you tried integrating with respect to y _first_ and then with respect to x ? Sometimes reversing the order of integration helps.
Doug Hull on 22 Jul 2011
Does the function make sense to integrate in that direction?

John D'Errico on 9 Oct 2020
No. You cannot first use a numerical integration to first integrate with respect to one variable, and THEN hope to use a symbolic integral on a second variable. The numerical integration produces a number. It will NOT be a symbolic function of y or any other variable.
Can you interchange the order of the integration? Yes, under some circumstances. As long as the limits of integration are not impacted, then you should typically be able to integrate on y first, and then use a numerical tool to integrate that result over x. And in some cases, even if the limits of integration are an issue, you may be able to resolve the problems. All of this would be specific to the case at hand however.