Expert: Paul Klarreich - 11/9/2006

Question
As I go through my study guide I am finding some questions that perplex me hopefully you can help me with this one.

Find the area enclosed by y=e^x, y=e^-x, and x=1.

Thanks in advance for any help you can offer.

Answer
Questioner:  Gary
Category:  Calculus
 
Subject:  Graph curves
Question:  As I go through my study guide I am finding some questions that perplex me hopefully you can help me with this one.

Find the area enclosed by y=e^x, y=e^-x, and x=1.

Thanks in advance for any help you can offer.
...........................................
Hi, Gary,

Another 'App of Int' problem?  I'm sure you used your graphing calculator on this one

and found that the two graphs meet at (0,1), giving you a 'triangle-ish'-shaped region, bounded:

A. On top by  y = e^x
B. Bottom by  y = e^-x
C. Left by x = 0
D. Right by x = 1, as specified.

So you look for your 'sample piece'.  [Remember that?]  It will be a rectangular region with:

Height = top - bottom = e^x - e^-x
Width = dx

So your integral is:

(1
| (e^x - e^-x) dx
)0

= e^x + e^-x  from 0 to 1.

= (e^1 + e^-1) - (e^0 + e^0)

= e + 1/e - 2

And you can try your calculator on that.
Mine gives  1.0861612696304875569558112415141