Results 1 to 2 of 2

Math Help - Rotated infinite region

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    Arizona
    Posts
    7

    Rotated infinite region

    Rotated infinite region-image.jpgFor this problem I started with part a by saying that the area diverges by using the p test where p=1. For the second half I found the area of a cross sectional washer to be pi(1 - (1/x^2))delta x. Taking the integral of this from to infinity would result in an infinitesimally large area - an infinitesimally small area, thus resulting in another divergence. Is this correct? Why should I have been surprised by the answer?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Feb 2013
    From
    Saudi Arabia
    Posts
    435
    Thanks
    84

    Re: Rotated infinite region

    Bikerboy

    integrate from 1 to infinity the function 1/x to obtain +infinity .this means that surprisingly the area enclosed by the graph 1/x and the x-axis from 1 to infinity is extremely large though it is not seem to be so!. The curve 1/x aproaches the x-axis....it is an asymptote and they meet at a point very far away...infinity.

    Rotating the graph of curve y=1/x over the x-axis you have to integrate the function π(1/x)^2 from 1 to infinity but surprisingly you will find the volume to be equal to π

    This is the surprise....the curve has an infinite area but if rotated it generates a finite volume...

    Minoas
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 17th 2011, 09:40 PM
  2. [SOLVED] Region of convergence of an infinite series
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: July 28th 2010, 11:51 AM
  3. Rotated about the...
    Posted in the Calculus Forum
    Replies: 9
    Last Post: May 2nd 2010, 05:47 PM
  4. volume rotated about y=2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 13th 2009, 01:05 PM
  5. Volume for region rotated around the x-axis
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 29th 2009, 11:11 PM

Search Tags


/mathhelpforum @mathhelpforum