Results 1 to 3 of 3

Math Help - Help with finding volumes of rotated curves

  1. #1
    Member
    Joined
    Apr 2009
    Posts
    85

    Help with finding volumes of rotated curves

    Hey I was recently introduced to the disc, cylindrical shell, and washer methods and I don't understand them fully mostly because it's difficult for me to imagine the shapes created when rotating curves and i dont know which method to use. Here is the problem:

    Consider the solid obtained by rotating the region bounded by the given curves about the x-axis.
    Find the volume V of this solid.

    I decided to use the disc method and set up my integral like so:

    \pi\int(16-4x^2)^2dx

    With -2 and 2 for the limits of integration...solving this yields 64 \pi but i cant get the correct volume.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    1) I always try to do it both ways, just to emphasize the concepts in my mind.

    2) That is not 64\pi. Please demonstrate your work.

    3) You have it set up exactly correctly. Try the integral again.

    4) And the other way: 2\pi \int_{0}^{16}y \left[ 2\sqrt{\frac{16-y}{4}}\right] \;dy. See if you get the same answer.

    5) Please learn to observe an exploit symmetries. The limits of your integral could have been [0,2] with the result multiplied by 2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2009
    Posts
    85
    Thank you for the helpful reply i see what i did, or rather, didn't do.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 8th 2011, 06:36 AM
  2. Replies: 6
    Last Post: August 5th 2011, 05:01 AM
  3. [SOLVED] find the volume of the curves rotated about the x-axis
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 11th 2010, 12:46 PM
  4. Volumes rotated about the x-axis.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 16th 2010, 03:19 PM
  5. Mathematica and volumes of rotated solids
    Posted in the Math Software Forum
    Replies: 3
    Last Post: September 26th 2008, 05:23 AM

Search Tags


/mathhelpforum @mathhelpforum