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Homework Help: Area between curves y=((e^x)-(e^-x))/2 and y=2e^-x

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Area between curves y=((e^x)-(e^-x))/2 and y=2e^-x for -1 < x < 2

    2. Relevant equations
    I know the formula is the integral of ( u(x)-l(x) )dx, but I'm having a lot of trouble trying to integrate this.

    integral from -1 to ln(5)/2: (((2e^-x)-((e^x)-(e^-x))/2))dx + int. ln(5)/2 to 2: (((e^x)-(e^-x))/2-2e^-x)dx

    3. The attempt at a solution
    I graphed everything and solved for x (intersection at x=ln(5)/2) but have been unable to get the right answer after that point. I tried splitting the formula into smaller integrals by linearity to simplify integration but consistently got the wrong answer for that.
    Should I try to split it up again? Or am I missing a pretty easy integration in here?
  2. jcsd
  3. Mar 10, 2010 #2
    well, I'm trying this question again so just thought i'd bump with a little question to get started.

    since the first half of the area integral works out to be:

    A = int: {2e-x-(ex-e-x)/2}dx

    can I just separate it into:

    A = int: 2e-xdx - int: (ex-e-x)/2dx

    or is the fact that the two formulas are in brackets rule out the linearity subtraction rule?
  4. Mar 10, 2010 #3
    k got this one too, bury this thread as desired
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