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## #1 2007-07-11 14:21:14

Krizalid
Member
Registered: 2007-03-09
Posts: 51

### Integral Marathon

Hi y'all!!

I wanna start an

Rules are easy: person which solves an integral, may post the next one but he must have the approval of the person which proposed the previous integral if the answer is correct or not.

Compute

Best regards!

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## #2 2007-07-11 15:00:07

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Integral Marathon

sec(x) - tan(x) + x + C?

A logarithm is just a misspelled algorithm.

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## #3 2007-07-11 15:09:15

Krizalid
Member
Registered: 2007-03-09
Posts: 51

### Re: Integral Marathon

That's correct.

You can post the next one.

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## #4 2007-07-11 19:37:34

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Integral Marathon

Last edited by mikau (2007-07-11 19:51:38)

A logarithm is just a misspelled algorithm.

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## #5 2007-07-11 21:28:53

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Integral Marathon

Krizalid wrote:

but he must have the approval of the person which proposed the previous integral if the answer is correct or not

Why not just differentiate back and check? Also, is there any need to use blatantly sexist language?

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## #6 2007-07-12 04:26:22

Krizalid
Member
Registered: 2007-03-09
Posts: 51

### Re: Integral Marathon

mikau wrote:

sec(x) - tan(x) + x + C?

Sorry, you have to show us your solution (I dunno what I was thinking that I didn't ask you that).

JaneFairfax wrote:

JaneFairfax wrote:

Why not just differentiate back and check? Also, is there any need to use blatantly sexist language?

Well, actually when I was writing I didn't realize of that.

If you don't mind, please limit to make all type of disagreeable commentary. There're forms and forms to request the things.

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## #7 2007-07-12 06:44:20

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Integral Marathon

Thats right, Jane. Good job! Looks like you're next as soon as you show your solution.

and here's my solution to the first problem.

∫sin x /(1 +sin x) dx =  ∫[-sin^2(x) + sin x ]/(1 - sin^2(x)) dx

=  ∫ -sin^2(x)/cos^2(x) - sin(x)/cos^2(x) dx

=  ∫ -tan^2(x) + sec(x)tan(x) dx

=  ∫ 1 -sec^2(x) + sec(x)tan(x)dx = x - tan(x) + sec(x) + C  QED.

Last edited by mikau (2007-07-12 08:26:04)

A logarithm is just a misspelled algorithm.

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## #8 2007-07-12 09:38:46

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Integral Marathon

JaneFairfax wrote:

Also, is there any need to use blatantly sexist language?

http://www.xkcd.com/c145.html

Which reminds me:

http://www.xkcd.com/c263.html

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #9 2007-07-12 10:49:35

MathsIsFun
Registered: 2005-01-21
Posts: 7,657

### Re: Integral Marathon

That last comic was superb!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #10 2007-07-12 14:05:42

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Integral Marathon

i'll say!

We're still waiting for you to post the next one, Jane!

A logarithm is just a misspelled algorithm.

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## #11 2007-07-13 05:23:52

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Integral Marathon

Why did the vector cross the road?
It wanted to be normal.

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## #12 2007-07-14 21:17:53

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

­­­

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## #13 2007-07-15 04:30:54

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

### Re: Integral Marathon

Doesn't this sort of thing also belong in Puzzles and Games? It is kind of a game, after all, it does follow the rule of most forum-based games.

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## #14 2007-07-15 07:01:45

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Integral Marathon

Maybe it used to, but now it belongs in the "Jane is mean " section.
We don't have one of those yet, so it might as well stay here.

Why did the vector cross the road?
It wanted to be normal.

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## #15 2007-07-15 22:40:31

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Integral Marathon

mathsyperson wrote:

Jane is mean

Why?

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## #16 2007-07-15 23:30:31

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Integral Marathon

is that meant to be interpreted as:

or

?

The Beginning Of All Things To End.
The End Of All Things To Come.

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## #17 2007-07-16 00:03:11

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Integral Marathon

Oops, typo. That should read "mathsy is dumb "
For some reason I read that as e^-x², and thought you were giving an impossible one. The didn't help either.

Why did the vector cross the road?
It wanted to be normal.

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## #18 2007-07-16 00:18:44

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Integral Marathon

Last edited by JaneFairfax (2007-07-16 00:22:43)

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## #19 2007-07-16 00:22:26

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Integral Marathon

mathsyperson wrote:

For some reason I read that as e^-x², and thought you were giving an impossible one. The didn't help either.

is continuous for all real x and is therefore integrable for all real x. There is a theorem that states that all continuous functions are Riemann integrable.

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## #20 2007-07-16 03:53:38

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Integral Marathon

Now Jane, go again.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #21 2007-07-16 10:53:20

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Integral Marathon

Yes.

Ive also seen

I believe you can integrate an absolutely convergent series term by term within its radius of convergence, and the result would be another absolutely convergent series?

Rickys turn.

Last edited by JaneFairfax (2007-07-16 11:02:54)

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## #22 2007-07-16 12:16:01

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Integral Marathon

Pass.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #23 2007-07-16 12:19:35

Krizalid
Member
Registered: 2007-03-09
Posts: 51

### Re: Integral Marathon

I forgot to mention that don't post integrals which don't have a primitive function in elementary terms.

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## #24 2007-07-16 12:32:51

mikau
Member
Registered: 2005-08-22
Posts: 1,504

### Re: Integral Marathon

Pass? :-( Who's next?

this was in one of my books, i could never figure out how to do it. i think its non elementary.

Last edited by mikau (2007-07-16 12:36:11)

A logarithm is just a misspelled algorithm.

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## #25 2007-07-16 14:09:23

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Integral Marathon

Not impossible but it involves complex analysis.  I would suggest picking a different integral.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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