1. Not finding help here? Sign up for a free 30min 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!

Finding the volume of the integral

  1. Jan 20, 2008 #1
    I need to find the volume of the solid obtained by rotating the region bounded by given curves about a specified line.
    [tex]y = ln x, y = 1, y = 2, x = 0;[/tex] about the x-axis

    since there are 3 "y"s
    I'm not sure how to use
    [tex]V = \int_{a}^{b} {A(x)}{dx}[/tex]

    Thank you in advance~
     
  2. jcsd
  3. Jan 20, 2008 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    What you need to, is to find out how the cross-section actually looks like, for example by DRAWING it.

    However, here's how you could proceed analytically:

    Since for x<e, ln(x)<1, and will tend to negative infity as x trundles towards 0, it follows that this segment cannot be part of our region.

    Thus, for 0<=x<=e, the cross-section lies between y=1 and y=2.

    When x=e^2, ln(e^2)=2, so that for e<=x<=e^2, we have that our region lies between y=ln(x) and y=2.

    Use this info to complete the problem.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Finding the volume of the integral
Loading...