Finding region bounded by curves

1. Jan 27, 2006

superelf83

Hi. I'm new here. :) I was wondering if anyone could help me out with this problem....
i'm supposed to find the region bounded by:
y=x+1
y=e^-x
x=1

i think i should find the other point of intersection but i forgot to do that (i haven't taken a math course for about 4 years).

2. Jan 27, 2006

maverick6664

It's just

$$\int_0^1 (x+1-e^{-x}) dx = (\frac 1 2 x^2 + x + e^{-x})\vert_0^1 = 1/2+e^{-1}$$

3. Jan 27, 2006

HallsofIvy

Staff Emeritus
Find the region or find the area of the region?

"i think i should find the other point of intersection but i forgot to do that "
Forgot to do that or forgot how to do that?

The region is bounded by the three curves y= x+ 1, y= e-x and x= 1. It should be easy to see that y= x+ 1 and y= e-x cross at (0, 1). Of course, y= x+ 1 and x= 1 cross at (1, 2). Finally, y= e-x and x= 1 cross at (1, e-1).