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quick maths question - integration

Discussion in 'General Discussion' started by dean_ham, 8 May 2006.

  1. dean_ham

    Hitman

    Joined: 3 Jul 2005

    Posts: 884

    Location: S.Wales

    im having a blank moment here, and i have no answers...

    if i intergrate 2/x, do you take the x up so its 2x^-1, then integration that will make it 2x^0 / 0, which will make it 0?

    cheers
     
  2. Dave

    Mobster

    Joined: 30 Oct 2004

    Posts: 4,937

    Location: Sacramento CA

    Nope.

    The integral of 2/x dx is 2lnx.

    The integral of a 1/x function, or f'(x)/f(x) is lnx, and not a constant. :)


    edit/ don't forget the "test" by deriving your result; d/dx(2lnx) = (2)(1/x) = 2/x, so it's right. d/dx(0) . . . ;)
     
  3. Nitefly

    Man of Honour

    Joined: 24 Sep 2005

    Posts: 33,017

    Yep, 1/x always becomes lnx

    So 10/x would be 10lnx etc. :)
     
  4. dean_ham

    Hitman

    Joined: 3 Jul 2005

    Posts: 884

    Location: S.Wales

    cheers i looked at 1/x on my tables of intergrals, but thought nahhh lol

    Thanks :D

    as u can see i need a new maths teacher ha ha :D or a bit more revising :p
     
  5. spirit

    Wise Guy

    Joined: 18 Oct 2002

    Posts: 1,885

    good luck with p2/3 :)
     
  6. Vonhelmet

    Caporegime

    Joined: 28 Jun 2005

    Posts: 48,107

    Location: On the hoods

    Not to mention degree level calculus :eek:
     
  7. spirit

    Wise Guy

    Joined: 18 Oct 2002

    Posts: 1,885

    :confused:
     
  8. McDaniel

    Capodecina

    Joined: 15 Aug 2003

    Posts: 19,872

    Location: Southend-on-Sea

    i hated those exams with a passion
     
  9. spirit

    Wise Guy

    Joined: 18 Oct 2002

    Posts: 1,885

    lol i only really disliked p5 'cause u actually had to think about stuff, but it was fun i guess really
     
  10. McDaniel

    Capodecina

    Joined: 15 Aug 2003

    Posts: 19,872

    Location: Southend-on-Sea

    i didnt have P5 \0/

    I enjoyed maths until a-level but i did have possible the worst teacher in the world, who got her own calculations wrong and the class had to correct her :o
     
  11. spirit

    Wise Guy

    Joined: 18 Oct 2002

    Posts: 1,885

    fair enough my alevel teacher for pure was weird - he was some kind of maths genius (in terms of like olympiad questions and stuff) but would always get stuff like basic alevel integration wrong lol but he taught us alot of tricks..
    He also creeped me out, cause he used to put music on whilst doing maths and dance (he is gay) and it was wierd really wierd.
     
  12. McDaniel

    Capodecina

    Joined: 15 Aug 2003

    Posts: 19,872

    Location: Southend-on-Sea

    Sounds Hilarious tho :D
     
  13. Arcade Fire

    Banned

    Joined: 26 Jan 2005

    Posts: 5,426

    Location: Cambridge

    Eh?

    My tip when doing integrations: remember that differentiation is always, ALWAYS easier than integration. You can differentiate practically anything, but some things are a complete pain in the arse to integrate.

    What's the moral of this? When you've just done a tricky integration, take 20 seconds out to differentiate your answer and see if you get what you started with. It's such a simple check to make, but so many people get integrations wrong without noticing it because they don't check their answer afterwards.

    If anyone saves some marks in an exam because of this, you can send money to my Paypal address. ;)
     
  14. spirit

    Wise Guy

    Joined: 18 Oct 2002

    Posts: 1,885

    on the same vein if you simply cant see a way to integrate (esp with ** p123 type questions) think of a something you differentiate to get that result {may not work if they use trickery with trig identities :p}...

    not sure if that made sense or will be useful to anyone :D
     
  15. Vonhelmet

    Caporegime

    Joined: 28 Jun 2005

    Posts: 48,107

    Location: On the hoods

    N/m.