![]() |
An HP48/49 CAS question - Printable Version +- HP Forums (https://archived.hpcalc.org/museumforum) +-- Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum-1.html) +--- Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum-2.html) +--- Thread: An HP48/49 CAS question (/thread-44483.html) |
An HP48/49 CAS question - Valentin Albillo - 10-17-2003 Hi everybody. Not owning any HP48/49 model, there's no immediate way for me to test this, so I'd appreciate if any of you HP48/49 owners would try this for me and post here the results.
The question is: what result does the HP48/49 symbolic algebra system produce for the following indefinite integral: Integral[ sin(x^n) . dx ]where n is a constant ? Specifically, I'm interested to know if it does produce some kind of exact closed result, in terms of known functions (elementary or not). I'm not interested in Taylor-series-expansion based results or any other non-closed approximations (not to mention purely numerical results). In case it can't produce a closed result for general, arbitrary n, I would then be interested to know if it can produce a closed result for some particular values of n, and if so, the specific values of n it can solve. I would expect it to be able to produce a closed result for n = 0 and n = 1 at the very least, but what about other values of n, both integer and non-integer (n = 2, 3, ..., 1/2, 1/3, ...) ? What about negative values of n (n = -1, -2, ..., -1/2, ...) ?
Thanks in advance for any results or comments and best regards from V.
Re: An HP48/49 CAS question - Werner Huysegoms - 10-17-2003 Hi Valentin.
Cheers, Werner
Re: An HP48/49 CAS question - Valentin Albillo - 10-17-2003 Werner posted: "The 49 cannot solve any but the most trivial of these integrals (ie with N=0 or 1). All the rest are simply returned in integral form."
Best regards from V.
Re: An HP48/49 CAS question - rolando - 10-17-2003 ValentÃn:
INTVX(SIN(X^N)) = INT(SIN(EXP(N*LN(X))) I did no try the IBP (integration by parts) command because the function to be integrated must be expressed as a product of functions. The ROM in the emulator was 1.18 It seems that this is too much for the HP49G CAS. Rolando
Re: An HP48/49 CAS question - hugh - 10-17-2003 you're expecting a bit much arent you. these integratals are mostly only in terms of special functions (like complex gamma, sinc, and fresnel) which arent even there. except for the cases n = 0, 1 and 1/2. interstingly the case n = -1, is close to one of my numerical tests: integrate(cos(1/x), 0, 1) numerically or otherwise. so far no calculator has even got close (-0.0844109505)
Re: An HP48/49 CAS question - hugh - 10-17-2003 there's some more. 1/m (m = 1,2...) are also representable since int(sin(x^n), dx) can be solved when int(x^n sin(x), dx) is soluble. i'd be interested to know if these come out of the 48/49, using alg48, for example.
Re: An HP48/49 CAS question - Werner Huysegoms - 10-20-2003 Hi Valentin. I did use a real 49G in the process: The Xt stuff is a change of variable and the 4x's way of saying it can't solve the integral.
Cheers, Werner Re: An HP48/49 CAS question - Valentin Albillo - 10-20-2003 Thanks Werner, it's more or less what I expected and what would be reasonable, by the way. The fact that it manages to solve the n=1/2 case is encouraging. I've always been somewhat amazed by the fact that sin(sqrt(x)) is elementarily integrable while sin(x^2) is not. One would tend to expect exactly the opposite, as the square root function seems more 'irrational', so to speak, than the simple, polynomial, 'square' function :-)
Best regards from V.
|