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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.

Let's start with an easy one

Compute

Best regards!

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Integral Marathon

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

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A logarithm is just a misspelled algorithm.

Krizalid

Member

Registered: 2007-03-09

Posts: 51

Re: Integral Marathon

That's correct.

You can post the next one.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Integral Marathon

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

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A logarithm is just a misspelled algorithm.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Integral Marathon

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?

Krizalid

Member

Registered: 2007-03-09

Posts: 51

Re: Integral Marathon

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).

Show your solution too.

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.

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)

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A logarithm is just a misspelled algorithm.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Integral Marathon

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

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"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..."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Integral Marathon

That last comic was superb!

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

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!

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A logarithm is just a misspelled algorithm.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integral Marathon

Zach agrees.

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Integral Marathon

­­­

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.

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.

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Integral Marathon

Jane is mean

Why?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Integral Marathon

is that meant to be interpreted as:

or

?

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

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.

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Integral Marathon

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Integral Marathon

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.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Integral Marathon

Now Jane, go again.

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"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..."

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)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Integral Marathon

Pass.

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"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..."

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.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Integral Marathon

Pass? :-( Who's next?

how about

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)

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A logarithm is just a misspelled algorithm.

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.

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"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..."