Using Math like that here is cheating, as the point is using J--for finding things, like derivatives etc. It's OK to interpret results with Math, but not to use math to get results.
So here is pure J, analytical and complete solution. -~/ (^&_1.001 d. _1) 1 _ 1000 > From: Don Guinn <[email protected]> > > Given: > f =: 3 'x^_0.001' > > The integral of f as a J expression ignoring an arbitrary constant is > if =: _1000*^&_0.001 > > So the integral of f between a lower limit (ll) and an upper limit (ul) > -~/if ll,ul > > -~/if 1 _ > 1000 > > -~/if 1 1e300 > 498.813 > > So the calculation using adapt is correct as far as it goes. But as > the integral is close to becoming unbounded, going to 1e300 is not > nearly far enough to be correct as the upper bound goes to unbounded. > > Gotta know the math behind the problem and not just blindly accept an > answer from a computer. > > > On Thu, Jan 7, 2010 at 12:26 AM, Oleg Kobchenko wrote: > >> From: DIETER ENSSLEN > > > >> > >> yes, intriguing, mysterious, baffling > >> > >> but the answer is 1000, not 498.813 > > > > Tools don't contain answers, they merely enable > > people to derive them. That's exactly what I did. > > I was too lazy to recall a paper and pencil method or > > find the answer on the internet. I used J, and only J > > to find the answer. And the answer, obtained with J, > > is correct. > > > > > >> From: Oleg Kobchenko > >> > >> > From: DIETER ENSSLEN > >> > > >> > Also, I just found out to my disappointment that J won't handle > >> > relatively > >> > simple definite integrals like 1/x^1.001 from 1 to infinity > >> > >> Using induction and forgiving numerical limitations, > >> it should probably be 1000. > > ^^^^ > >> > >> load'~system/packages/math/integrat.ijs' > >> > >> ^&_1.5 adapt 1 1e200 > >> 2 > >> ^&_1.2 adapt 1 1e200 > >> 5 > >> ^&_1.1 adapt 1 1e200 > >> 10 > >> > >> ^&_1.05 adapt 1 1e300 > >> 20 > >> ^&_1.02 adapt 1 1e300 > >> 50 > >> ^&_1.01 adapt 1 1e300 > >> 99.9 > >> > >> ^&_1.005 adapt 1 1e300 > >> 193.675 > >> ^&_1.002 adapt 1 1e300 > >> 374.406 > >> ^&_1.001 adapt 1 1e300 > >> 498.813 > > > > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
