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Volume of region roated about specified axi

  1. Mar 8, 2013 #1
    1. The problem statement, all variables and given/known data

    y = e^(-x), y = 0, x = -1, x = 0, about x = 1

    2. Relevant equations



    3. The attempt at a solution
    2pi∫ (1-x)(e^(-x) dx from -1 to 0

    =2pi∫ e^(-x) -x*e^(-x) dx from -1 to 0
    =2pi(-e^(-x) - ∫x*e^(-x) dx from -1 to 0
    u=x
    du=dx
    dv=e^(-x)dx
    v=-e^(-x)
    2pi(-e^(-x)-(-xe^(-x) +∫e^(-x)dx))
    2pi(-e^(-x) +xe^(-x) +e^(-x))
    2pi(xe^(-x)) from -1 to 0
    2pi(e)

    is this right?
     
  2. jcsd
  3. Mar 8, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Seems ok to me.
     
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