1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Volume generated

  1. Jul 19, 2006 #1
    A question here:
    Given two curves

    The region in the first quadrant that is bounded by the y-axis and these two curves is rotated through one complete revolution about the x-axis. Calculate the exact volume of the solid generated.

    My problem is, in the first quadrant, y=1+2e^(-x) seems touching the x-axis at [tex]x=\infty[/tex], so how do we find the volume?
    Last edited: Jul 19, 2006
  2. jcsd
  3. Jul 19, 2006 #2
    You sure you copied the problem correctly?
  4. Jul 19, 2006 #3
    Thanks, you are right that the question has not been copied correctly. I have changed
    Please refer to the original question again. Very sorry for any inconvenience caused.
  5. Jul 19, 2006 #4


    User Avatar
    Science Advisor

    The two curves cross at (0,3), of course, and the region under the two curves is symmetric about the y-axis. However, if that really is the correct formula, because y goes to 1 as x goes to [itex]\infty[/itex], and as x goes to [itex]-\infty[/itex], the volume generated contains an infinitely long cylinder of radius 1 and so is not finite.
  6. Jul 19, 2006 #5


    User Avatar
    Homework Helper

    A start

    The two curves are [tex]y=e^{x}[/tex] and [tex]y=1+2e^{-x}[/tex] which intersect when [tex]e^{x}=1+2e^{-x}[/tex] multiply by e^x to get [tex]e^{2x}-e^{x}-2=0[/tex] so by the quadratic formula we have [tex]e^{x}=2[/tex] or [tex]x = \log {2}[/tex] so the curves meet at the point (log 2, 2). The other boundary is the y-axis so the bounded area is now finite (see attached plot) and to be rotated about the x-axis, so do an integral :smile: . --Ben

    Attached Files:

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook