Ask Your Question
1

I don't know why Sage return 0 for integrate(sin(2*x).abs(),(x,0,pi)) when its value is 2

asked 2014-12-14 09:25:05 -0600

Arturo gravatar image

updated 2014-12-14 13:59:37 -0600

tmonteil gravatar image

When I try integrate(sin(x).abs(),(x,0,pi)) the program return the same thing. The numerical integration is correct, the program return (1.9999999999999998, 2.220446049250313e-14). I don't know if it is a bug or what. Any help? I have tried sage 6.2, 6.3, 6.4.1

Mathematica can do It without any problem http://www.wolframalpha.com/input/?i=...

Neither Sympy nor Maxima can't compute this.

edit retag flag offensive close merge delete

3 answers

Sort by ยป oldest newest most voted
1

answered 2014-12-14 13:59:11 -0600

tmonteil gravatar image

They are indeed some issues with integrals involving absolute values, see a list here At least in your case no wrong answer is returned.

edit flag offensive delete link more

Comments

@tmonteil: The question's title suggests that a wrong answer is indeed returned, even if the text of the question counterbalances that by the fact that numerical integration is correct.

slelievre gravatar imageslelievre ( 2015-02-05 02:50:39 -0600 )edit
0

answered 2015-02-03 08:41:30 -0600

marguin gravatar image

With Sage-4.7, integrate(abs(sin(t)),t,0,pi) returns 2 as expected.

edit flag offensive delete link more
0

answered 2014-12-15 10:10:25 -0600

kcrisman gravatar image

Interestingly,

sage: integrate(abs(sin(x)),x)
-(2*arctan(sin(x)/(cos(x) + 1))*sin(x)/(cos(x) + 1) - log(2))*sgn(1/(cos(x) + 1))*sgn(sin(x)) - log(2*sin(x)^2/(cos(x) + 1)^2 + 2)*sgn(1/(cos(x) + 1))*sgn(sin(x)) + log(sin(x)^2/(cos(x) + 1)^2 + 1)*sgn(1/(cos(x) + 1))*sgn(sin(x)) + 2*(sin(x)/((sin(x)^2/(cos(x) + 1)^2 + 1)*(cos(x) + 1)) + arctan(sin(x)/(cos(x) + 1)))*abs(sin(x))/abs(cos(x) + 1)

Not that this is all that useful, because if we call this f then f(pi) has division by zero error, and based on comments elsewhere it is probably wrong in any case. I have to admit I am surprised this isn't doable, though. See this ticket 17511 but there are lots of places this question has recurred.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2014-12-14 09:25:05 -0600

Seen: 511 times

Last updated: Feb 03 '15