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        riddles >> medium >> Another integral
        
(Message started by: ThudanBlunder on Oct 21^st, 2008, 6:13pm)

Title: Another integral
Post by ThudanBlunder on Oct 21^st, 2008, 6:13pm

8
Evaluate http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/int.gifln(9 - x) / [ln(9 - x) + ln(x - 3)].dx
4

Title: Re: Another integral
Post by 1337b4k4 on Oct 22^nd, 2008, 12:08am

[hide]substitute u = 12 - x to get http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/int.gifln(u - 3) / [ln(9 - u) + ln(x - u)]dx So the original integral plus this one add up to the http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/int.gif1 from 4 to 8, which is 4. Thus the answer to the original is 2.[/hide]

Also, my math input isn't working :(
http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/int.gifhttp://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif
I can see other people's math just fine. This was working before... am I not formatting it right?

Title: Re: Another integral
Post by towr on Oct 22^nd, 2008, 1:50am

on 10/22/08 at 00:08:11, 1337b4k4 wrote:

I can see other people's math just fine. This was working before... am I not formatting it right?

Have you ticked the "Insert Symbols" box? If you don't use the "Add symbols" menu, and you don't quote a post that uses symbols, then you have to tick that box yourself (otherwise it's automatic).

Title: Re: Another integral
Post by 1337b4k4 on Oct 22^nd, 2008, 11:31am

There we go, thanks!

Title: Re: Another integral
Post by adnanmat on Nov 17^th, 2008, 11:08am

Hello

i am sorry but ı cant understood this problem

Could you explain me?

Title: Re: Another integral
Post by adnanmat on Nov 17^th, 2008, 11:17am

Hello

My name is Adnan Donmez from Turkey

I have problem with this integral problem

Can you explain me?

8
Evaluate ln(9 - x) / [ln(9 - x) + ln(x - 3)].dx
4

Title: Re: Another integral
Post by towr on Nov 17^th, 2008, 11:24am

If you select the orange area in 1337b4k4's post, you should be able to see his solution.
He makes a clever substitution, adds the two integrals, and then the solution is suddenly very simply.

Title: Re: Another integral
Post by adnanmat on Nov 17^th, 2008, 1:28pm

I saw him solution

But i cant understand

Title: Re: Another integral
Post by towr on Nov 17^th, 2008, 2:02pm

Make a substitution
ln(9 - x) / [ln(9 - x) + ln(x - 3)]
=> x=v
ln(9 - v) / [ln(9 - v) + ln(v - 3)]
=> v= 12-x
ln(9 - (12-x)) / [ln(9 - (12-x)) + ln((12-x) - 3)]
=>
ln(x-3) / [ln(x - 3) + ln(9-x)]
=>
ln(x-3) / [ln(9-x) + ln(x - 3) ]

(As for the rest of the integral, the boundaries are switched, but so is the direction of integration 4->8, 8->4, dx -> d(12-x)= -dx)

Add the original and new expressions together
ln(9 - x) / [ln(9 - x) + ln(x - 3)] + ln(x-3) / [ln(9-x) + ln(x - 3) ]
=>
[ln(9 - x) + ln(x-3)] / [ln(9 - x) + ln(x - 3)]
=>
1

Integrating over a constant is fairly simple, and will get you twice the value you're looking for.

Title: Re: Another integral
Post by adnanmat on Nov 17^th, 2008, 2:05pm

Thanks a lot