Results 1 to 5 of 5

Math Help - Volume of Revolution

  1. #1
    Banned
    Joined
    Aug 2008
    Posts
    530

    Volume of Revolution

    Find the volume of revolution of the region generated,

    bounded by graph y = 6 - 2x -x^2

    and the indicated line y = x + 6.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by Shyam View Post
    Find the volume of revolution of the region generated,

    bounded by graph y = 6 - 2x -x^2

    and the indicated line y = x + 6.
    rotated about a line? which one?
    Last edited by skeeter; April 3rd 2009 at 05:01 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by skeeter View Post
    rotated about a line? which one?
    rotated about line y = x+6
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by Shyam View Post
    rotated about line y = x+6
    here's the work I did:
    After solving the equations of parabola and line, I found their point of intersection.
    The point of intersection of parabola and line are (-3, 3) and (0, 6)

     V = \pi \int\limits_{ - 3}^0 {\left[ {\left( {6 - 2x - x^2 } \right)^2  - \left( {x + 6} \right)^2 } \right]} .dx \hfill \\

      = \pi \int\limits_{ - 3}^0 {\left[ {\left( {x^4  + 4x^3  - 8x^2  - 24x + 36} \right) - \left( {x^2  + 12x + 36} \right)} \right]} .dx \hfill \\

     = \pi \int\limits_{ - 3}^0 {\left[ {x^4  + 4x^3  - 9x^2  - 36x} \right]} .dx \hfill \\

      = \pi \left[ {\frac{{x^5 }}<br />
{5} + x^4  - 3x^3  - 18x^2 } \right]_{ - 3}^0  \hfill \\

     = \pi \left[ {\left( {\frac{{\left( { - 3} \right)^5 }}<br />
{5} + \left( { - 3} \right)^4  - 3\left( { - 3} \right)^3  - 18\left( { - 3} \right)^2 } \right) - \left( {0 + 0 - 0 - 0} \right)} \right] \hfill \\

       = \pi \left[ {\frac{{ - 243}}<br />
{5} + 81 + 81 + 162} \right] \hfill \\

      = \pi \left[ {\frac{{ - 243}}<br />
{5} + 324} \right] \hfill \\

      = \frac{{1377\pi }}<br />
{5} \hfill \\

    This answer seems too big to me. Is it correct?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by Shyam View Post
    rotated about line y = x+6
    what you have shown is the work required for a rotation of the region about the x-axis, not about the line y = x+6.

    this is correct ...

      = \pi \left[ {\frac{{x^5 }}<br />
{5} + x^4  - 3x^3  - 18x^2 } \right]_{ - 3}^0  \hfill \\
    one error in the integral evaluation below ... you did the FTC evaluation backwards, should be F(0) - F(-3)

     = \pi \left[ {\left( {\frac{{\left( { - 3} \right)^5 }}<br />
{5} + \left( { - 3} \right)^4 - 3\left( { - 3} \right)^3 - 18\left( { - 3} \right)^2 } \right) - \left( {0 + 0 - 0 - 0} \right)} \right] \hfill \\
    sign error in this next step ... +162 ?

       = \pi \left[ {\frac{{ - 243}}<br />
{5} + 81 + 81 + 162} \right] \hfill \\
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. volume of revolution
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: April 13th 2011, 05:53 AM
  2. Volume of Revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 16th 2009, 04:44 PM
  3. Volume of revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 5th 2009, 06:37 PM
  4. Volume by revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2009, 03:37 PM
  5. Volume of revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 22nd 2008, 11:09 AM

Search Tags


/mathhelpforum @mathhelpforum