I was wondering.. if you could help me calculate some integrals:
It's not for Homework or something, just my curiosity:
\displaystyle{\int}\sqrt[3]{x^2-1} dx
What would you suggest? I tried substitution, thou it seems to me useless.
Are these integrals common in tests and exams? I mean, they seem to me just pure mathematics, i.e. - no application, and I'm not sure, if that's not too much to ask from a student..
Thanks in Advance, Marin
HallsofIvy
Aug24-08, 02:23 PM
If it weren't for that "3", which I almost missed, I would say use a trig substitution. Since that won't work, I have to ask if you have any reason to think it does have an elementary anti-derivative? You must understand that "almost all" elementary integrands do not have an elementary anti-derivative. ("Elementary" here meaning made up of combinations of polynomials, roots, trig functions, exponentials, logarithms.)
Marin
Aug24-08, 02:30 PM
hmmmm, didn't think of that
Maybe it doesn't. That means, we have to integrate using power series, to get the series of the antiderivative, doesn't it?
tiny-tim
Aug24-08, 02:31 PM
Hello everyone!
I was wondering.. if you could help me calculate some integrals:
It's not for Homework or something, just my curiosity:
\displaystyle{\int}\sqrt[3]{x^2-1} dx
Hello Marin! :smile:
hmm… I get ∫(sinhu)5/3 du, which (like HallsofIvy :smile:) I don't think has a "elementary" anti-derivative. :frown:
Are these integrals common in tests and exams? I mean, they seem to me just pure mathematics, i.e. - no application, and I'm not sure, if that's not too much to ask from a student.
If I were you, I'd just do the set examples, and similar ones.
Your course has been specially designed to make the best use of your time. :wink:
There are ways of integrating such functions (well, there must be, mustn't there? :rolleyes:), but they're in a different ball-park, and you won't be able to guess them from what you already know.
Your professors will induct you into that ball-park when and if the time is appropriate …
trust your professors, and follow the course! :smile:
Marin
Aug24-08, 02:52 PM
Well I guess I have no other choice but wait and follow the profs :)
Sometimes I tend to search for solutions of examples not to my level.. but what can I do for it - they just don't leave me in peace.., despite I think of self-teaching as not very appropriate