symbolic integration

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R yan 2011-7-22

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回答： John D'Errico 2020-10-9

    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

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Walter Roberson 2011-7-22

Have you tried integrating with respect to y _first_ and then with respect to x ? Sometimes reversing the order of integration helps.

Doug Hull 2011-7-22

Does the function make sense to integrate in that direction?

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Answer 1

John D'Errico 2020-10-9

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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.