Area Bounded by Functions

[nasillmatic20]

Hello again everyone,

My problem is as follows:

Find the area of the region bounded by the functions y=e^(2-3x) , y=e^(2-x) , y=e^x

I understand that for regular bounded area problems, you take the integral of f(x) - g(x), but I have no idea how to do this for three separate functions... any help would be greatly appreciated!

 

[ChaoticLlama]

First of all, I would reccommed making a quick sketch of these three curves.
If you are having difficulty, trying using this site to assist with the graphs.

That should help you find the intersection points, and therefore the limits of integration as well as the functions included in both integrands.

TIP: You will need two integrals to solve this problem

 

[nasillmatic20]

Aha, I think I think I got it.... please correct me if I'm wrong:

I'll take the integral of [e^(2-x) - e^x] on the interval of 0 to their POI and subtract the integral of [e^(2-3x) - e^x] on the interval of 0 to their POI

 

[pka]

Always, always, graph the question.\(\displaystyle \L
\int\limits_0^{1/2} {\left[ {\left( {e^{2 - x} } \right) - \left( {e^{2 - 3x} } \right)} \right]dx} + \int\limits_{1/2}^1 {\left[ {\left( {e^{2 - x} } \right) - \left( {e^x } \right)} \right]dx}\)