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Math Help - Volume of solids of revolutions

  1. #1
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    Volume of solids of revolutions

    I am trying to solve a question in my integration topic using volumes of solids of revolutions the attatchment shows my workings and the part I would like some guidance with
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  2. #2
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    Quote Originally Posted by jimss2 View Post
    I am trying to solve a question in my integration topic using volumes of solids of revolutions the attatchment shows my workings and the part I would like some guidance with
    Hi jimss2,

    y=2x^3

    \frac{y}{2}=x^3

    x=\left(\frac{y<br />
}{2}\right)^{\frac{1}{3}}

    as x and y are positive in the region of interest.

    Both methods you mentioned are equivalent.
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  3. #3
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    Thankyou for your reply it was very helpful I am still struggling with integrating x=(y/2)^1/3 as I do not know what to do when bringing the power down as the 2 is already there each method I try give me the wrong answer
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  4. #4
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    For part 2,

    0.5\int_{y=0}^{54}{\pi}x^2dy=\frac{{\pi}}{2}\int_{  0}^{54}\left(\frac{y}{2}\right)^{\frac{2}{3}}dy

    integrating this, we bring out the denominator under y first, then raise the power of y by 1
    and divide by the new power

    \frac{{\pi}}{2}\int_{0}^{54}\left(\frac{1}{2}\righ  t)^{\frac{2}{3}}y^{\frac{2}{3}}dy=\frac{{\pi}}{2}\  left(\frac{1}{4}\right)^{\frac{1}{3}}y^{\frac{2}{3  }+\frac{3}{3}}\frac{1}{\frac{2}{3}+\frac{3}{3}}

    evaluated from y=0 to y=54

    \frac{{\pi}}{2}\left(\frac{1}{4}\right)^{\frac{1}{  3}}y^{\frac{5}{3}}\left(\frac{3}{5}\right)

    from 0 to 54

    =\frac{3{\pi}}{10}\left(\frac{1}{4}\right)^{\frac{  1}{3}}54^{\frac{3}{5}}-0
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  5. #5
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    thankyou this has been very helpful
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