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

1. Mar 9, 2010

### shft600

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. Mar 10, 2010

### shft600

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. Mar 10, 2010

### shft600

k got this one too, bury this thread as desired