1. Part (a) y = ex y = ln x 1 -1 2 1 1/2 Area = (ex - ln x) dx
= or 1.223 1 -1 2
y = ex
y = ln x

2. To find the volume, we need to use the washer method.
Part (b) 1 2 3 4
To find the volume, we need to use the washer method.
R = (4 - ln x) r = (4 - ex )
V = p [(4 - ln x)2 - (4 - ex)2] dx
1/2 1
Volume = p or

3. Part (c)
h(x) = ex – ln x
The absolute maximum & absolute minimum of h(x) will occur either at an endpoint or where h’(x) = 0.

4. Part (c)
h(x) = ex – ln x
Endpoints:
h(1/2) = e(1/2) – ln (1/2)
= 2.342
= 2.718
h(1) = e(1) – ln (1)

5. Graph both functions, then find their intersection point.
Part (c)
h(x) = ex – ln x
Critical points:
h( )
= 2.330
h’(x) = ex – 1/x
Graph both functions, then find their intersection point.
ex – 1/x = 0

6. Part (c)
h(1/2)
= 2.342
h(1)
= 2.718
h( )
= 2.330
Absolute Min
Absolute Max