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

  • Thread starter shft600
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  • #1
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Homework Statement



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

Homework 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

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?
 

Answers and Replies

  • #2
24
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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?
 
  • #3
24
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k got this one too, bury this thread as desired
 

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