# Application of Integration- help!

1. Apr 27, 2010

### skylit

1. Let f be the function given by f(x) = ex + 1, where the region R is bounded by the graph of f(x), the y-axis, and the horizontal line y=4.

2. Relevant equations
a. Find the area of region R.
b. A vertical line x=h, where h>o is chosen so that the area of the region bounded by f(x), the y-axis, the horizontal line y=4, and the line x=h is half the area of the region R. What is the value of h?
c. Find the volume of the solid formed when region R is rotated about the line y=4.
d. A horizontal line y=k, where k is greater than 4 is chosen so that the volume of the solid formed when region R is rotated about the line y=k is twice the volume of the solid found in part (c). Set up, but do not evaluate, an integral expression in terms of a single independent variable which represents the volume of this solid.

3. The attempt at a solution
I found part a and b..
a.) 1.296
b.) h=.361

I'm drawing a blank about c, when I draw the graph reflected about y=4, would it be illogical to simply multiply the area given in (a) by 2?
And I can't move on without being sure of c.. so that is where I am, haha.

2. Apr 27, 2010

### zachzach

No it would not be logical. If you multiply an area by two it is still an area, not a volume. Do you know how to find the volume?

3. Apr 27, 2010

### skylit

In this case, is it.. volume of a sphere? Or half a sphere?

4. Apr 27, 2010

### zachzach

No. I'm assuming you have drawn the function and found the region (if not do so). Imagine rotating the region around y = 4. To me it looks more like half of a football.

5. Apr 27, 2010

### zachzach

6. Apr 27, 2010

### skylit

It doesn't ring a bell at all..yes I drew the graph, and rotated about y=4. The first impression I got was a semicircle, but I realize what you're saying about an oval-like shape, which completely disproved my sphere theory haha

7. Apr 27, 2010

### skylit

If this has anything to do with cross sections, then I am in desperate need of help (I could never grasp it)

8. Apr 27, 2010