Application of Integration- help

[skylit]

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

Homework 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.

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.

 

[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?

 

[skylit]

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

 

[zachzach]

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

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.

 

[zachzach]

Have you learned solids of revolution in class? Basically you split the thing into infinitesimal disks and add them up. http://en.wikipedia.org/wiki/Solid_of_revolution

 

[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

 

[skylit]

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

 

[zachzach]

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

Yes it does. This website is good and will help you http://archives.math.utk.edu/visual.calculus/5/volumes.5/index.html. It seems to me you are not picturing the rotation the right way.