Please explain result

03292018, 12:19 PM
Post: #1




Please explain result
After a restart, entering: int(sin(x),x,0,∞), repeatedly, produces the results shown in the image. What is meant by "bounded_function(n)+1", where n increments by 2, after each entry?
[attachment=5792] 

03292018, 05:24 PM
Post: #2




RE: Please explain result
Hm, "undef" would be a reasonable answer, as the integral does not converge. Boundedfunction is clear, so the number that is increased by 2 is interesting.
Arno 

03292018, 05:40 PM
Post: #3




RE: Please explain result
Found boundedfunction in an xcas document:
For regular series expansion, order_size is a bounded function, but for non regular series expansion, it might tend slowly to infinity, for example like a power of ln(x). So its left over by the tried taylor expansion of sin(x) to get the integral done, then simply returned as the result, but the argument isn't explained. Arno 

03292018, 06:19 PM
Post: #4




RE: Please explain result
It's a divergent integral, limit does not exist, but I didn't grasp the idea of "boundary_function(n)+1", where the n is always even. What does the "n" tell us, and is the +1, just there to represent a constant? Sometimes the way these things are taught varies by country, but I haven't encountered this kind of result anywhere.


03292018, 06:57 PM
(This post was last modified: 03292018 06:59 PM by Arno K.)
Post: #5




RE: Please explain result
I think the one simply is (cos(0)), so the antiderivative is first evaluated at its lower bound, n may be an exponent used by taylor, using cosine instead of sine makes it increase by 6, but here Bernard may have an answer.
Arno 

03292018, 07:32 PM
Post: #6




RE: Please explain result
I introduced bounded functions in order to solve limits like
limit(sin(x+1/x)sin(x),x,inf) 

03292018, 07:54 PM
Post: #7




RE: Please explain result
What does the function value represent?
bounded_function(2)+1 

03302018, 06:14 AM
Post: #8




RE: Please explain result
Exactly that: a bounded function + 1 (the +1 comes from evaluation of cos at 0).


03302018, 08:31 AM
Post: #9




RE: Please explain result  
03302018, 10:57 AM
Post: #10




RE: Please explain result
Interesting ... I shut down the system last night, and this morning when I turned it back on and ran the emulator, all the preexisting "bounded_function(n)" entries had changed to "undef+1"
Why does the number increment by 2 each time similar integrals are entered? Further divergent entries like: int(cos(x),x,0,∞); int(sin(x),x,0,∞); still result in bounded_function(2*n) (I am using n to represent the number of divergent integrals entered). Can programmers use that information for some suitable purpose? 

03302018, 11:07 AM
Post: #11




RE: Please explain result
No. I'm thinking of replacing bounded_function by undef in the limit output.


03302018, 11:44 AM
Post: #12




RE: Please explain result
It seems like undef would be more meaningful, Parisse, and thank you, very much, for your explanations, and guidance!
Dale 

03302018, 11:50 AM
Post: #13




RE: Please explain result
Change has been committed.


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