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This is not a mathematical question, but just a matter of terminology.

I don't understand why so many people (especially on MSE) want to solve integrals. It makes sense for me (linguistically speaking) to solve an equation or to solve a problem, but definitely not to solve an integral: instead, I would just say compute.

So, I would like to know if "to solve an integral" is correct English. Needless to say, English is not my native language...

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In math a lot of things can be re-written in equation form. I would agree that you aren't strictly solving anything when you integrate $\int f(x) \,dx$ but that is equivalent to "solving" the equation $F(x) = \int f(x)\, dx$ for $F(x)$. – Brad Jun 11 '14 at 15:57
I'm not a native english speaker, but I don't think 'solve' is an appropriate term for what you describe. I think the confusion comes from misconception of the terms (solve, compute and variants) themselves and possibly from the fact (?) that in some languages the natural translation of 'solve' leads to the concept of 'compute' in english. There's also the possibility that you could look at it as "Solve the problem" and the problem actually is an integral. – Git Gud Jun 11 '14 at 15:58
Another French asking the same question… – LeGrandDODOM Jun 11 '14 at 15:59
@brad You remind me of the basket-weaver who told me all mathematical problems reduce to basket weaving. After all, if the solution to your problem is $X$, then a basket in the shape of $X$ is the solution to your problem. – Dan Piponi Jun 11 '14 at 16:07
@G.T.R Thanks for the link. I should have checked before. – Etienne Jun 11 '14 at 16:22
up vote 13 down vote accepted

It is wrong in English to say "solve an integral". We should say "evaluate an integral" or "compute an integral" instead.

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I forgot "evaluate"... thanks! – Etienne Jun 11 '14 at 16:27
I tend to think that "compute" applies only to definite integrals, but that may just be me. "Evaluate" seems like the correct choice for finding a non-integral expression of an integral. – Kyle Strand Jun 11 '14 at 23:13

In the Russian it is not correct. Russians use word 'take' instead.

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That's interesting! In French we would never say "take". – Etienne Jun 11 '14 at 16:23
oddly enough, in English we "take" derivatives but not integrals.... – KutuluMike Jun 11 '14 at 18:58
Indeed, see e.g. this message on a Russian forum: "Решить интеграл - невозможно!", i.e. "It is impossible to solve an integral". This hints to the frequent use of this incorrect term by Russian students (and I have heard really many of them say so). Usually they are those who just want to pass the math class and never return to it. – Ruslan Jun 11 '14 at 18:58

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