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It's a classic question, tha answer is
Let's perform a double integration solution:
The rest follows. Easy, huh ¿?
Have you sketched the region where the integral is taken? That'd help.
Hola, jaja
Ya está resuelta en aquél foro. (I'm not gonna post the URL for not makin' SPAM.)
Tony: you should be patient, post your problems in one forum first, if you see that it's not solved, try with another ones.
You'll get quickly the desired.
I couldnt believe that nobody saw that the best way to solve the equation is not to expand everything out into a mess but to exploit the symmetry of the equation and use a substitution in this case the equation is symmetrical about r−2, so the substitution is R = r−2. I had to register on their forum just to tell them how it should be done.
Don't worry, there're smart guys.
In any case, I hadn't seen such thread
Of course you should see something wrong with that.
Do you know www.mathhelpforum.com ? He's actually posting the same questions there and takin' solutions from another posters to show them right here.
Well, whatever.
Dear perash, you recently posted the same problem on MHF and you received an answer, did you see it?
Okay, I've got it.
And rewrite
The rest follows constructin' a double integral.
It's similar to #1. Use the following parameter:
From there construct a double integral, the rest follows.
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As for the third one, let me think it a little bit, looks like hard.
Beautiful problems!
Evaluate
Construct a double integral and reverse the integration order,
Now
And
where as by Taylor's theorem.Thus,
.
You stole this from a guy of another forum, what a shame.
You didn't even change any word.
Let
Consider
Since
You may go on from there.
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If you know Frullani's Integral, you can get the result directly.
Once I get it off the ground I think there may be a lot of Spanish-speaking visitors directed to this forum.
Spanish is my mother language ^^
By the way, do you like "disfrutalasmatematicas.com" ... ?
I like "disfrutalasmates.com".
Short & "mates" sounds better than "matemáticas".
Just wonderin'.... why instead creating a domain you create, here, a spanish section?
Thank you.
Also, the command \implies does not work. It's the same as \Longrightarrow.
Evaluate
The integral can be rewritten as
Substitute
Evaluate
Substitute
Make another substitution defined by
Yeah, it's a little application about a formula that I recently proved.
Evaluate
Another attempt it is to define the following integral
Since
Or substitute
and from there construct a double integral to tackle the problem.
Or Frullani's Integral may be useful.
No, I mean
This looks nice, but when using \frac, there's not enough space.
That's why eqnarray environment is perfect for alignment.
Could the Admin. activate the eqnarray environment ¿?
\begin{eqnarray*}
\end{eqnarray*}
That'd be nice.
Id suggest changing to polar co-ordinates.
To do that, split the original square into two triangles:
Aha, you like: www.disfrutalasmates.com?
I am thinking it would be good to translate some of the mathsisfun.com website to Spanish, but what would "Math is Fun" be in Spanish
"Matematicas es divertida" ... ? Not a good domain name: matematicasesdivertida.com
Any Ideas?
Ohh!!
That'd be nice!
You like spanish ¿?
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I think we can call it "Mate es entrete".
"Entrete" means "Fun", actually, the complete spanish word is "Entretenida", but it is a little large for the domain name.
I have lots of nice smileys, if you want them, I can show them to you.