I want to know whether "partial integration" exists analogous to partial differentiation in ordinary calculus for functions of several variables.
Does "partial integration" exist analogous to partial differentiation (in general)?
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1partial integration is synonym for [integration by parts](http://en.wikipedia.org/wiki/Integration_by_parts) – 2011-11-07
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3If I understand the question correctly, I'd say yes. For example, you can compute $\int x^2+3y^2 \, dy= yx^2+y^3 +C(x)$ (the constant of integration becomes an arbitrary function of $x$). – 2011-11-07
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3I think you're looking for [line integrals](http://en.wikipedia.org/wiki/Line_integral), possibly along a coordinate line. – 2011-11-07
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5@pedja No, partial derivatives are looking at the change in only one coordinate. Integration by parts is undoing the product rule. – 2011-11-07
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0@Graphth [partial integration](http://en.wikipedia.org/wiki/Partial_integration) – 2011-11-07
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2@pedja I see, but the point of the question is to find an integration that is analogous to partial derivatives. Is integration by parts analagous to partial derivatives? I don't think so. So, it's just that the OP doesn't know the correct term. Your comment is saying that term already exists but doesn't describe what the OP is asking about? – 2011-11-07
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1@Graphth,I just pointed out on wrong use of the term – 2011-11-07
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0@pedja Okay, sorry, I misunderstood. – 2011-11-07
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0@pedja To the best of my knowledge, "partial integration" used to refer to integration by parts is just a mistranslation of the German term and as a calque for other foreign terms. In my American courses "partial integration" and "integration by parts" have always been distinct concepts, the former actually being an inverse operation to partial differentiation. – 2016-11-05