Results 1 to 9 of 9

Math Help - volume of revolution

  1. #1
    Member
    Joined
    Apr 2014
    From
    canada
    Posts
    244

    volume of revolution

    i have done the part a, for b , i use the key in the (circled part equation ) in to calculator .. my ans is also different form the ans given. is my concept correct by the way? volume of revolution-dsc_0138-3-1-.jpgvolume of revolution-dsc_0139-2-1-.jpgvolume of revolution-dsc_0140-2.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Feb 2013
    From
    Saudi Arabia
    Posts
    443
    Thanks
    86

    Re: volume of revolution

    I haven't see in your calculations to multiply by π .
    I found after integration from 0 to 1/2 V = 5.0477...
    check it and do not forget to multiply by π.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2014
    From
    canada
    Posts
    244

    Re: volume of revolution

    ok, noted my mistake
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Apr 2014
    From
    canada
    Posts
    244

    Re: volume of revolution

    i redo the question, now got stuck here... which part is wrong?volume of revolution-dsc_0141-2-1-.jpg
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602

    Re: volume of revolution

    For one thing, a volume by revolution is given by $\displaystyle \begin{align*} V = \pi \int_a^b{\left[ f(x) \right] ^2 \, dx} \end{align*}$. You still don't have $\displaystyle \begin{align*} \pi \end{align*}$...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Apr 2014
    From
    canada
    Posts
    244

    Re: volume of revolution

    using calcultor, before times pi, the ans should be 1.60675, by my ans only 1.5... which part is wrong? this almost drive me crazy!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602

    Re: volume of revolution

    $\displaystyle \begin{align*} V &= \pi \int_0^{\frac{1}{2}}{ \left( 1 + \frac{1}{4x^2 + 1} \right) ^2 \, dx } \\ &= \pi \int_0^{\frac{\pi}{4}}{ \left\{ 1 + \frac{1}{4 \left[ \frac{1}{2}\tan{(\theta)} \right] ^2 + 1 } \right\} ^2 \, \frac{1}{2}\sec^2{(\theta)}\,d\theta } \textrm{ after making the substitution } 2x = \tan{(\theta)} \\ &= \frac{\pi}{2}\int_0^{\frac{\pi}{4}}{ \left[ 1 + \frac{1}{\tan^2{(\theta)} + 1 } \right] ^2 \sec^2{(\theta)}\,d\theta } \\ &= \frac{\pi}{2}\int_0^{\frac{\pi}{4}}{ \left[ 1 + \frac{1}{\sec^2{(\theta)} } \right] ^2 \sec^2{(\theta)}\,d\theta} \\ &= \frac{\pi}{2} \int_0^{\frac{\pi}{4}}{ \left[ 1 + \cos^2{(\theta)} \right] ^2 \sec^2{(\theta)} \,d\theta } \\ &= \frac{\pi}{2} \int_0^{\frac{\pi}{4}}{ \left[ 1 + 2\cos^2{(\theta)} + \cos^4{(\theta)} \right] \sec^2{(\theta)}\,d\theta } \\ &= \frac{\pi}{2} \int_0^{\frac{\pi}{4}}{ \sec^2{(\theta)} + 2 + \cos^2{(\theta)} \,d\theta } \\ &= \int_0^{\frac{\pi}{4}}{ \sec^2{(\theta)} + 2 + \frac{1}{2} + \frac{1}{2}\cos{(2\theta)} \,d\theta } \\ &= \frac{\pi}{2} \int_0^{\frac{\pi}{4}}{ \sec^2{(\theta)} + \frac{5}{2} + \frac{1}{2}\cos{(2\theta)} \,d\theta } \\ &= \frac{\pi}{2} \left[ \tan{(\theta)} + \frac{5}{2}\theta + \frac{1}{4}\sin{(2\theta)} \right]_0^{\frac{\pi}{4}} \\ &= \frac{\pi}{2} \left\{ \left[ \tan{ \left( \frac{\pi}{4} \right) } + \frac{5}{2}\left( \frac{\pi}{4} \right) + \frac{1}{4}\sin{ \left( \frac{\pi}{2} \right) } \right] - \left[ \tan{(0)} + \frac{5}{2} \left( 0 \right) + \frac{1}{4}\sin{(0)} \right] \right\} \\ &= \frac{\pi}{2} \left[ \left( 1 + \frac{5\pi}{8} + \frac{1}{4} \right) - \left( 0 + 0 + 0 \right) \right] \\ &= \frac{\pi}{2} \left( \frac{5}{4} + \frac{5\pi}{8} \right) \\ &= \frac{5\pi}{8} \left( 1 + \frac{\pi}{2} \right) \\ &= \frac{5\pi}{16} \left( 2 + \pi \right) \end{align*}$
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Apr 2014
    From
    canada
    Posts
    244

    Re: volume of revolution

    thank you very much... i should have done in this way instead of expand the y^2
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602

    Re: volume of revolution

    Quote Originally Posted by delso View Post
    thank you very much... i should have done in this way instead of expand the y^2
    Expanding first should also have worked though...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. volume of revolution
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 24th 2009, 06:37 AM
  2. Volume of Revolution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 18th 2009, 10:05 AM
  3. Volume of revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 5th 2009, 07:37 PM
  4. Volume of Revolution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 5th 2009, 02:50 PM
  5. Volume of Revolution
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 29th 2009, 08:14 PM

Search Tags


/mathhelpforum @mathhelpforum