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

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    hear hear wonkey!
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    (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.
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    (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!!!)
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    (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
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    (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
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    (Original post by mabs)
    George Explain!!!!!
    Wait a mo, theres an error in my working, i get 2e-2 if you run through it...
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    (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.
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    (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!
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    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
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    comeon guys! help me out here!
    i'm pssing ma pants
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    (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.
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    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.
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    (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
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    (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?
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    (Original post by mabs)
    comeon guys! help me out here!
    i'm pssing ma pants
    flip........tell me people wots 'lne'?? 1?
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    (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?
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    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) !!
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    (Original post by wonkey)
    flip........tell me people wots 'lne'?? 1?
    yes
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    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
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    someone show me the u and v dash method, geebee, d/dx x (wt is that???) - first line of working
 
 
 
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