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Homework Help: Application of Integration- help!

  1. Apr 27, 2010 #1
    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. jcsd
  3. Apr 27, 2010 #2
    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?
     
  4. Apr 27, 2010 #3
    In this case, is it.. volume of a sphere? Or half a sphere?
     
  5. Apr 27, 2010 #4
    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.
     
  6. Apr 27, 2010 #5
  7. Apr 27, 2010 #6
    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
     
  8. Apr 27, 2010 #7
    If this has anything to do with cross sections, then I am in desperate need of help (I could never grasp it)
     
  9. Apr 27, 2010 #8
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