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Homework Help: Integration by parts and substitution help

  1. Feb 25, 2009 #1
    Integration by parts and substitution help!!

    1. The problem statement, all variables and given/known data


    ∫0
    -1 e ^√x+1




    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 25, 2009 #2

    HallsofIvy

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    Science Advisor

    Re: Integration by parts and substitution help!!

    I'm sorry, but I simply cannot figure out what that integral is intended to be.

    Is that [tex]\int_{-1}^0 e^{\sqrt{x+1}} dx[/tex] or [tex]\int_{-1}^0 e^{\sqrt{x}+ 1} dx[/tex] or [tex]\int_{-1}^0 e^{\sqrt{x}}+ 1 dx[/tex]?

    If it is the first, take [itex]u= \sqrt{x+1}= (x+1)^{1/2}[/itex] so that [itex]du= (1/2)(x+1)^{-1/2}dx[/itex] so that [itex](x+1)^{1/2}du= u du= dx[/itex]. When x= -1, u= 0, when x= 0, u= 1 The integral becomes
    [tex]\int_0^1 ue^{u}du[/tex]
    and can be done by "integration by parts".

    If the second, write it as [tex]e\int_{-1}^0 e^{\sqrt{x}}dx[/tex] and let [itex]u= \sqrt{x}[/itex].

    If the third, write it as [tex]\int_{-1}^0 e^{\sqrt{x}}dx+ \int_{-1}^0 dx[/tex].
     
    Last edited by a moderator: Feb 25, 2009
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