| View previous topic :: View next topic |
| Author |
Message |
commutative
Guest
|
 Posted: Sun, 8 Oct 2006 12:26:55 UTC Post subject: A Definite Integral |
 |
|
Suppose we know  Find  |
|
| Back to top |
|
 |
bird_of_paradox
Member of the 'S.O.S. Math' Hall of Fame
Joined: 22 Nov 2005
Posts: 394
Location: Australia - the world's suburb.
|
| Posted: Sun, 8 Oct 2006 14:58:59 UTC Post subject: Re: A Definite Integral |
|
|
| commutative wrote: | | Suppose we know Find |
That's screaming out to use parts, I think...
I'm not 100% sure of that last step... seems a bit weird, evaluating a function at the limits twice like that. Anyway, substituting in A for that ugly integral:
Hardest thing about that was coding the flippin' LaTeX... 2 min on paper followed by 15 min typing, dammit. The only things that would mess with that too severely are the evaluating the function twice at the limits thing (mentioned above), or the pole at  ... are they anything?
_________________
'I'm a fireman.
You don't understand.
I don't put fires out,
I start them.' |
|
| Back to top |
|
|
commutative
Guest
|
| Posted: Sun, 8 Oct 2006 18:09:37 UTC Post subject: Re: A Definite Integral |
|
|
| bird_of_paradox wrote: | That's screaming out to use parts, I think...
|
unfortunately, what you got is not correct bird! by parts will give you this:
so ... maybe by parts is not a good idea here.
| Quote: |
Hardest thing about that was coding the flippin' LaTeX... 2 min on paper followed by 15 min typing, dammit. |
totally agree! :)
| Quote: | | ... or the pole at ... are they anything? |
 so there's nothing to worry about. |
|
| Back to top |
|
|
sean39
Member of the 'S.O.S. Math' Hall of Fame
Joined: 22 Feb 2004
Posts: 646
Location: 40.47N 73.58W
|
| Posted: Mon, 9 Oct 2006 00:31:55 UTC Post subject: Re: A Definite Integral |
|
|
| commutative wrote: | | Suppose we know Find |
By the Fundamental Theorem of Calculus:
Now we can do integration by parts:
_________________
"If I have not seen as far as others, it is because giants were standing on my shoulders." - Hal Abelson |
|
| Back to top |
|
|
bird_of_paradox
Member of the 'S.O.S. Math' Hall of Fame
Joined: 22 Nov 2005
Posts: 394
Location: Australia - the world's suburb.
|
| Posted: Mon, 9 Oct 2006 07:29:39 UTC Post subject: Re: A Definite Integral |
|
|
| sean39 wrote: |
By the Fundamental Theorem of Calculus:
|
Uhmm... A is constant with respect to x, so  .
Anyway, I just plotted the integrand (shoulda done that before  ), and it's strictly negative (the argument of the log < 1), so the area under the curve couldn't be zero. It has a root at x=0, another one where where  , and then goes down towards  at  .
Still messing about with this...
_________________
'I'm a fireman.
You don't understand.
I don't put fires out,
I start them.' |
|
| Back to top |
|
|
sean39
Member of the 'S.O.S. Math' Hall of Fame
Joined: 22 Feb 2004
Posts: 646
Location: 40.47N 73.58W
|
| Posted: Mon, 9 Oct 2006 07:37:34 UTC Post subject: |
|
|
_________________
"If I have not seen as far as others, it is because giants were standing on my shoulders." - Hal Abelson |
|
| Back to top |
|
|
sean39
Member of the 'S.O.S. Math' Hall of Fame
Joined: 22 Feb 2004
Posts: 646
Location: 40.47N 73.58W
|
| Posted: Mon, 9 Oct 2006 17:42:25 UTC Post subject: Re: A Definite Integral |
|
|
| commutative wrote: | | Suppose we know Find |
_________________
"If I have not seen as far as others, it is because giants were standing on my shoulders." - Hal Abelson |
|
| Back to top |
|
|
commutative
Guest
|
| Posted: Mon, 9 Oct 2006 19:25:35 UTC Post subject: Re: A Definite Integral |
|
|
| sean39 wrote: |  |
sadly, this is not true! 
well, the indefinite integral of ln(sinx), x*ln(sinx), x^2*ln(sinx), ... don't
have nice forms, i.e. can not be found in terms of elementary functions.
but what about definite integrals? we know that:
pretty well-known: 
probably less-known:  |
|
| Back to top |
|
|
sean39
Member of the 'S.O.S. Math' Hall of Fame
Joined: 22 Feb 2004
Posts: 646
Location: 40.47N 73.58W
|
| Posted: Mon, 9 Oct 2006 21:56:28 UTC Post subject: Re: A Definite Integral |
|
|
| commutative wrote: | | sean39 wrote: | |
sadly, this is not true!
well, the indefinite integral of ln(sinx), x*ln(sinx), x^2*ln(sinx), ... don't
have nice forms, i.e. can not be found in terms of elementary functions.
but what about definite integrals? we know that:
pretty well-known:
probably less-known: |
Someone please erase this post from my permanent record. 
_________________
"If I have not seen as far as others, it is because giants were standing on my shoulders." - Hal Abelson |
|
| Back to top |
|
|
commutative
Guest
|
| Posted: Mon, 9 Oct 2006 22:26:12 UTC Post subject: Re: A Definite Integral |
|
|
| sean39 wrote: | | Someone please erase this post from my permanent record. :cry: |
it's ok, it's just a mistake. take it easy! :) |
|
| Back to top |
|
|
|
FAQ 
Search 
Memberlist 
Usergroups
Register
Profile 
Log in to check your private messages 
Log in 
