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Integrals with e

  1. Sep 16, 2011 #1
    1. The problem statement, all variables and given/known data
    \begin{equation} \int_{-1}^{1} e^{u+1} \end{equation}

    2. Relevant equations


    3. The attempt at a solution

    I really seem to struggle with any problems with e in them. I think I may have missed some of the basic rules or something, but I can't seem to find what I missed.

    My guess on this one would be to rewrite the equation into:

    \begin{equation}\int_{-1}^{1} e^{u} e^{1}\end{equation}

    I know that the integral of [itex]e^{u}[/itex] is [itex]e^{u}[/itex] but I don't know how to integrate [itex]e^{1}[/itex]. I'm not even sure if I rewrote the problem correctly. I know that the answer is [itex]e^{2}-1[/itex] but I can't seem to figure out how to get there.

    I thought maybe [itex]e^{1}[/itex] would just integrate like a normal function giving [itex]1/2e^{2}[/itex] but I couldn't get it to work out with that either.

    I'm totally lost with these e functions. What am I doing wrong?
     
  2. jcsd
  3. Sep 16, 2011 #2

    gb7nash

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    Homework Helper

    This is a commonly known rule:

    [tex]\int af(x) dx = a\int f(x) dx[/tex]

    for constant a. Knowing this now...
     
  4. Sep 16, 2011 #3
    I don't understand how that rule applies exactly.
     
  5. Sep 16, 2011 #4

    gb7nash

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    Homework Helper

    Think more about it. Is e1 a constant?
     
  6. Sep 16, 2011 #5
    Ok. I got it now. I wasn't thinking of [itex]e^{1}[/itex] as a constant. Thanks for the help.
     
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