Results 1 to 2 of 2

Math Help - Rotating a figure...

  1. #1
    Member
    Joined
    Feb 2010
    From
    United States
    Posts
    155
    Thanks
    1

    Rotating a figure...

    Find the volume of f(x)= 2-x^2 and g(x)=1 when rotated around the line y= 1


    Alright, so when I do this I get the answer 86(pi)/15. According to the teacher's answer, it should be 16(pi)/15. I can't figure out what I did wrong, so can someone please solve this out and let me know what I messed up? Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    454
    Quote Originally Posted by bobsanchez View Post
    Find the volume of f(x)= 2-x^2 and g(x)=1 when rotated around the line y= 1


    Alright, so when I do this I get the answer 86(pi)/15. According to the teacher's answer, it should be 16(pi)/15. I can't figure out what I did wrong, so can someone please solve this out and let me know what I messed up? Thank you!
    V = \pi \int_{-1}^1 [(2-x^2)-1]^2 \, dx

    V = 2\pi \int_0^1 (1-x^2)^2 \, dx

    V = 2\pi \int_0^1 1 - 2x^2 + x^4 \, dx

    V = 2\pi \left[x - \frac{2x^3}{3} + \frac{x^5}{5}\right]_0^1

    V = 2\pi \left[1 - \frac{2}{3} + \frac{1}{5}\right] = 2\pi \cdot \frac{8}{15} = \frac{16\pi}{15}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Finding the Angle in this Figure (see the figure)
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 19th 2011, 02:44 PM
  2. Rotating object
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 13th 2011, 11:33 PM
  3. Replies: 3
    Last Post: October 21st 2010, 08:46 AM
  4. Replies: 2
    Last Post: June 4th 2010, 07:02 AM
  5. Replies: 1
    Last Post: October 7th 2008, 01:18 AM

Search Tags


/mathhelpforum @mathhelpforum