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I often have trouble getting Wolfram|Alpha to compute definite integrals with variable bounds, and I'm wondering whether I'm missing something.

Some examples: $\int_a^b \sin x\mathrm dx$ and $\int \arcsin x \mathrm dx$ work fine; $\int_0^a \arcsin x \mathrm dx$ already requires extra time to finish; and $\int_a^b \arcsin x \mathrm dx$ doesn't compute even with extra time.

I'm thinking it probably has something to do with the conditions on the bounds, since there are conditions for the arcsine but not for the sine. It could be that W|A is having a hard time figuring out the conditions by itself; if so, how could I help it along?

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    I usually write something like "integrate xdx with 02011-07-13
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    But that specifies the bounds; I want to specify conditions/assumptions on the bounds.2011-07-13
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    I did not try your case but I had (and stil have) W|A behaving differently in Firefox and Internet Explorer.2011-09-23

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Yes, in Mathematica directly specifying conditions reduces computation time and sometimes allows to obtain a result at all. Mathematica input Integrate[ArcSin[x],{x,a,b},Assumptions->{-1<=a gets a result, but somewhat strange one, the integral is considered as indefinite.

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    Thanks -- it seems W|A can't handle that input -- do you happen to know how I can specify such assumptions to W|A?2011-07-13
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    That's very strange. I did press the link. I tried it again now, and I got the correct result, and then a few seconds later it gets replaced with a large list of suggestions what to try ("different phrasing or notations" etc.) Does the result stay around in your browser?2011-07-13
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    Bizarre -- I tried it again several times, and around the third time the result stayed.2011-07-13
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    @joriki: Well, very strange indeed. I get the correct result and there is a progress bar and after some progress it starts complaining. Also there is a mysterious "+constant" term appearing in the otherwise correct solution -- well, you can add *some* constants and get *a* correct result, but definitely not arbitrary ones :) [ **Added** I couldn't get the result to stay so far]2011-07-13
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    @joriki I have Opera, result stays. The correct form seems to be `Assuming[-1<=a2011-07-13
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    Yes, `Assuming[]` is usable in Wolfram Alpha, but not the `Assumptions` option for `Integrate[]`. I am not entirely sure why, either...2011-07-14
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    @Andrew: Thanks again for your answer -- I've accepted it, since no-one seems to know a more failsafe approach. In some cases I got results this way that I couldn't get before (sometimes even without the "indefinite integral" problem, e.g. for [$1/(1+x^2)$](http://www.wolframalpha.com/input/?i=Integrate%5B1%2F%281%2Bx%5E2%29%2C%7Bx%2Ca%2Cb%7D%2CAssumptions-%3E%7B-1%3C%3Da%3Cb%3C%3D1%7D%5D), but in others I didn't. It seems that Wolfram|Alpha is rather shaky in this area.2011-07-16
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    @joriki It seems that since WA understands syntax the only probable reason is time limit. So instability due perhaps to the amount of other requests processed at the moment. If this is the case there is nothing to be done.2011-07-16