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integration by parts

  • 09-06-2007 08:25PM
    #1
    lennykravitz
    Closed Accounts Posts: 22 ✭


    hey anyone have a solution for the 2000 question 8?????

    i'm trying to rape paper 2 material here to make up for my pathetic attempt at paper 1:eek:


Comments

  • #2
    Lucas10101
    Closed Accounts Posts: 630 ✭✭✭Lucas10101


    lennykravitz wrote:
    hey anyone have a solution for the 2000 question 8?????

    8
    (A)

    Ratio Test Question: Showing it's Divergent >1 for all values.

    (n+2)!/2^n+2

    Un => (n+2)!/2^n+2

    Un+1 => (n+3)!/2^n+3

    Un+1/Un => (n+3)!/2^n+3 * 2^n+2/(n+2)!

    (n+3)(n+2)!/2^n.2^3 * 2^n.2^2/(n+2)!
    Cancel the (n+2)! and the 2^n.

    (n+3)4/8

    => 4n +12/8

    lim 4n/n + 12/n divided by 8/n =>4

    4>0 Implies it's Divergent.

    I know it looks messy but write it down normally and it looks okay.


  • #3
    JC 2K3
    Closed Accounts Posts: 7,794 ✭✭✭JC 2K3


    int((e^2x)cosx.dx

    u = cosx
    du = -sinx.dx
    v = (e^2x)/2
    dv = e^2x.dx

    int((e^2x)cosx.dx = cosx(e^2x)/2 + int((e^2x)sinx.dx

    int((e^2x)sinx.dx

    u = sinx
    du = cosx.dx
    v = (e^2x)/2
    dv = e^2x.dx


    int((e^2x)sinx.dx = sinx(e^2x)/2 - int((e^2x)cosx.dx

    int((e^2x)cosx.dx = cosx(e^2x)/2 + sinx(e^2x)/2 - int((e^2x)cosx.dx
    2(int((e^2x)cosx.dx) = cosx(e^2x)/2 + sinx(e^2x)/2
    int((e^2x)cosx.dx = cosx(e^2x)/4 + sinx(e^2x)/4

    You need part 2?


  • #4
    JC 2K3
    Closed Accounts Posts: 7,794 ✭✭✭JC 2K3


    @Lucas

    It's always a good idea to read the title of a thread ;)


  • #5
    Lucas10101
    Closed Accounts Posts: 630 ✭✭✭Lucas10101


    lennykravitz wrote:
    hey anyone have a solution for the 2000 question 8?????

    Integration by Parts

    It's example 6 on the Text and Texts Book Integration by Parts section.


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