1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculus 1 Integration Problem

  1. Aug 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Calc I problem, so need to solve by calc 1 methods.

    ∫ (x-1)(x+1)^11 dx

    2. Relevant equations



    3. The attempt at a solution

    ∫ (x-1)(x+1)^11 dx

    U = x+1
    dU = dx
    x-1 = x+1-2 = U-2

    =∫ (U-2)U^11 dU

    =∫ U^12 dU - 2∫ U^11 dU

    =(1/13)U^13 - (1/6)U^12

    =(1/13)(x+1)^13 - (1/6)(X+1)^12

    ∫ (x-1)(x+1)^11 dx = (1/13)(x+1)^13 - (1/6)(X+1)^12



    The course ended already, this was the final test problem (on the test that ended already). I didn't understand how to do this one. I can check my answer and see it's wrong. My teacher won't be in until fall semester starts, so I can't ask him until then. I was already at full time, so Calc I was basically a free class I retook because it could boost GPA without being time consuming.
     
    Last edited: Aug 9, 2012
  2. jcsd
  3. Aug 9, 2012 #2
    [tex] \int (x-1)(x+1)^{11} dx \\ = \int x(x+1)^{11}-(x+1)^{11} dx \\ = \int [(x+1)-1](x+1)^{11}-(x+1)^{11} dx \\ = \int (x+1)^{12}-2(x+1)^{11} dx \\ = \frac{(x+1)^{13}}{13}-\frac{(x+1)^{12}}{6} +C[/tex]
     
  4. Aug 9, 2012 #3
    That seems to be the answer I got. Forgot all those constants on my answers >_<. When I take the derivative of that I get:

    (x+1)^12 - 2(x+1)^11 =/= (x-1)(x+1)^11

    I might be missing something here.
     
  5. Aug 9, 2012 #4
    But it is, isn't it?

    ##(x+1)^{12} - 2(x+1)^{11}##
    ##(x+1)(x+1)^{11} - 2(x+1)^{11}##
    ##(x+1)^{11}(x+1-2)##
    ##(x-1)(x+1)^{11}##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Calculus 1 Integration Problem
Loading...