Definite integral - "x - not defined" ? Options  Email this topic  Watch this topic  Print this topic » Normal Threaded

Previous Topic Next Topic

conrad		#1 Posted : 07 February 2019 16:08:26(UTC)
Rank: Newbie Groups: Registered Joined: 07/02/2019(UTC) Posts: 1		Hello, I have the following problem, trying to solve the definite integral int((3*x^3-x^2+2*x-4)/sqrt(x^2-3*x+2),dx,0,1): I get the error "x - not defined" and, of course, no result. If I change the limits to [0..401], I get a result (!) with no error message, but if I set the upper limit lower than 401, I get the error again... What is the reason for that? Thanks in advance for your replies. Conrad
User Profile View All Posts by User View Thanks

	Wanna join the discussion?! Login to your SMath Studio Forum forum account. New Registrations are disabled.

Jean Giraud		#2 Posted : 07 February 2019 17:13:06(UTC)
Rank: Guest Groups: Registered Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)		Originally Posted by: conrad If I change the limits to [0..401] The integrand is undefined @ x = 1
User Profile View All Posts by User View Thanks

Jean Giraud		#3 Posted : 07 February 2019 17:41:17(UTC)
Rank: Guest Groups: Registered Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)		Originally Posted by: Jean Giraud The integrand is undefined @ x = 1 Three verdicts in there: 1. Nothing will integrate that freak above x=1.9999999999999999999999999999 2. Nothing will integrate up to x=0.99999999999999999999999999999999 3. Can only integrate in reasonable range of the integrand. Interesting Classroom example ... always plot the integrand !!! IntegrateFreak.sm (8kb) downloaded 40 time(s).
User Profile View All Posts by User View Thanks

Jean Giraud		#4 Posted : 07 February 2019 18:32:46(UTC)
Rank: Guest Groups: Registered Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)		Hello Conrad, Often, it is possible to improve the Smath native Simpson integrator. Romberg is profitable in example 2 which looks easy from plotting the integrand, but finally is not so. Jean Integrate Romberg Technical.sm (52kb) downloaded 44 time(s).
User Profile View All Posts by User View Thanks

overlord		#5 Posted : 08 February 2019 09:50:36(UTC)
Rank: Advanced Member Groups: Registered Joined: 23/07/2013(UTC) Posts: 1,126 Was thanked: 507 time(s) in 338 post(s)		you can use maxima plugin if it is necessary. Regards
User Profile View All Posts by User View Thanks

Razonar		#6 Posted : 08 February 2019 12:33:47(UTC)
Rank: Advanced Member Groups: Registered Joined: 28/08/2014(UTC) Posts: 1,356 Was thanked: 815 time(s) in 516 post(s)		Hi. I think that here the point is how to handle avoidable discontinuities in SMath. Because integral and other operators or functions not accept the 'if' statement, you can use 'cases' in the definition of f, as this: Even this isn't the case, this other is more general for avoiding numerical issues with avoidable discontinuities: Best regards. Alvaro.
1 user thanked Razonar for this useful post.		on 08/02/2019(UTC)
User Profile View All Posts by User View Thanks

Razonar		#7 Posted : 08 February 2019 12:47:42(UTC)
Rank: Advanced Member Groups: Registered Joined: 28/08/2014(UTC) Posts: 1,356 Was thanked: 815 time(s) in 516 post(s)		About the other discontinuity, at x=2, I guess that you don't want to work with complexes. It's usual take the absolute vale of logs and roots in real analysis calculus. This other isn't avoidable discont, but can be handled in a similar way. discont_integral.sm (9kb) downloaded 41 time(s). Best regards. Alvaro.
3 users thanked Razonar for this useful post.		on 08/02/2019(UTC),  on 08/02/2019(UTC),  on 08/02/2019(UTC)
User Profile View All Posts by User View Thanks

uni		#8 Posted : 08 February 2019 14:33:05(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 10/11/2010(UTC) Posts: 1,494 Was thanked: 1274 time(s) in 745 post(s)		maple() also can do that. Edited by user 08 February 2019 14:38:33(UTC)  | Reason: Not specified
		Russia ☭ forever Viacheslav N. Mezentsev
		BLOG Twitter
2 users thanked uni for this useful post.		on 08/02/2019(UTC),  on 08/02/2019(UTC)
User Profile View All Posts by User View Thanks

Jean Giraud		#9 Posted : 08 February 2019 19:34:33(UTC)
Rank: Guest Groups: Registered Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)		Originally Posted by: uni maple() also can do that. maple [0..1] = -2.98126694400594 Mathcad 11 [0..1]= -2.98126694400554 Smath = -2.98126668567898 ... acc 10000 This is a case of singular end point
User Profile View All Posts by User View Thanks

Razonar		#10 Posted : 08 February 2019 21:16:38(UTC)
Rank: Advanced Member Groups: Registered Joined: 28/08/2014(UTC) Posts: 1,356 Was thanked: 815 time(s) in 516 post(s)		Originally Posted by: Razonar ... This other isn't avoidable discont, but can be handled in a similar way. Well, actually, the integral converges for x=2, as one can see in this wolfram result That's means that numerical procedure for computing int in SMath needs some improvements. Best regards. Alvaro.
User Profile View All Posts by User View Thanks

Jean Giraud		#11 Posted : 08 February 2019 22:13:59(UTC)
Rank: Guest Groups: Registered Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)		Originally Posted by: Razonar That's means that numerical procedure for computing int in SMath needs some improvements. That's an old long due request. At least, we have the adaptive from Carlos Romberg algo style works well, very useful too.
User Profile View All Posts by User View Thanks

Users browsing this topic

Guest