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# P3 Integration Dude's Hard One! Who Can Crack It?! watch

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1. hear hear wonkey!
2. (Original post by mabs)
BHAAL, (lnx)^2 means lnx all to the power 2 and u don't get wot u get when u use the chain rule.
Oh.
3. (Original post by wonkey)
i didnt know u could intergrate 'ln' functions?! how does du/dx + lnx become u = x(lnx - 1)???
You have to use by parts again

so INT ln x

du/dx=1
v=ln x

Voila!!!

Thanks guys btw - i managed to get the right ans now!!! I am so proud of myself!!! (yes i know everyone else got it before me - but don't burst my bubble!!!)
4. (Original post by wonkey)
i didnt know u could intergrate 'ln' functions?! how does du/dx + lnx become u = x(lnx - 1)???
INT 1*lnX

u = lnx u' = 1/x
v' = 1 v = x

xlnx - INT 1

xlnx - x
5. (Original post by Silly Sally)
You have to use by parts again

so INT ln x

du/dx=1
v=ln x

Voila!!!

Thanks guys btw - i managed to get the right ans now!!! I am so proud of myself!!! (yes i know everyone else got it before me - but don't burst my bubble!!!)

lol **** me..........P3 is really getting to me now
6. (Original post by mabs)
George Explain!!!!!
Wait a mo, theres an error in my working, i get 2e-2 if you run through it...
7. (Original post by George-W-Duck)
Wait a mo, theres an error in my working, i get 2e-2 if you run through it...

lol now thats just hilarious.
8. (Original post by George-W-Duck)
Wait a mo, theres an error in my working, i get 2e-2 if you run through it...
i got that too.. damned 2!
9. Can't remember wot integration by parts is, but anyway

We want Int (lnx)^2 dx

Well

d/dx x ( ln x )^2 = 2 x (ln x ) (1/x) + (ln x)^2

= 2 ln x + (ln x)^2

So Int (ln x)^2 = x ( ln x )^2 - Int( 2 ln x )

d/dx x ln x = ln x + 1

Int (ln x ) = x ln x - x

So

Int( ln x )^2 = x ( ln x )^2 - 2x ln x + 2x

From 1 to e

[e - 2e + 2e ] - [ 2 ] = e - 2
10. comeon guys! help me out here!
i'm pssing ma pants
11. (Original post by wonkey)
lol **** me..........P3 is really getting to me now
Its depressing me too, I have 4.5 day left before the exam and I can bring myself to revise for anthing else because im too worried about it. You would think that only needing 57/100 I would be relaxed etc... but it really is just stupidly difficult to do well in.
12. In this case we break the rule of allowing v' = lnx as we normally don't integrate lnx. So I wouldn't really be that depressed.
13. (Original post by mabs)
BHAAL, (lnx)^2 means lnx all to the power 2 and u don't get wot u get when u use the chain rule.

differential of (lnx)^2

y = t^2 t=lnx
dy/dt=2t dt/dx=1/x

dy/dx = 2t*1/x
= (2lnx)/x
14. (Original post by Silly Sally)
differential of (lnx)^2

y = t^2 t=lnx
dy/dt=2t dt/dx=1/x

dy/dx = 2t*1/x
= (2lnx)/x
Who are you trying to teach?
15. (Original post by mabs)
comeon guys! help me out here!
i'm pssing ma pants
flip........tell me people wots 'lne'?? 1?
16. (Original post by geebee2)
Can't remember wot integration by parts is, but anyway

We want Int (lnx)^2 dx

Well

d/dx x ( ln x )^2 = 2 x (ln x ) (1/x) + (ln x)^2

= 2 ln x + (ln x)^2

So Int (ln x)^2 = x ( ln x )^2 - Int( 2 ln x )

d/dx x ln x = ln x + 1

Int (ln x ) = x ln x - x

So

Int( ln x )^2 = x ( ln x )^2 - 2x ln x + 2x

From 1 to e

[e - 2e + 2e ] - [ 2 ] = e - 2
My friend has spoke of this method, what is it?
17. hold on a mo... go to calc101.com, and type ln^2[x] into the integrals bit...
I get the same answer, but when I put in values of e and 1, i Swear you get 2e-2 !! what the hell am i doing wrong?

-edit.. dont worry.. realised it's (ln x)^2 not (ln x^2) !!
18. (Original post by wonkey)
flip........tell me people wots 'lne'?? 1?
yes
19. it comes from integrating by parts on ln x

v = ln x
du/dx = 1
u = x
dv/dx = 1/x

uv - int (udv/dx) = xlnx - int(x/x) = xlnx - x

then using that you rightly integrate by parts to get:

x(lnx)^2 - xlnx - xlnx + x + x

then after tidyingm, sub in e and 1:

e(ln e)^2 - 2eln e + 2e - (1(ln1)^2 - 2ln1 + 2) = e - 2e+2e - 0 + 0 - 2 = e-2
20. someone show me the u and v dash method, geebee, d/dx x (wt is that???) - first line of working

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