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Math Help - Volume by shell method

  1. #1
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    Volume by shell method

    I'm trying to find the volume of this set of values

    y=x^3
    y=8
    x=0

    it is being rotated about the x-axis, the back of my text gives an answer of 768* pi/7 however i dont seem to be getting this value

    please help
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  2. #2
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    Quote Originally Posted by XyxFibonaccixyX View Post
    I'm trying to find the volume of this set of values

    y=x^3
    y=8
    x=0

    it is being rotated about the x-axis, the back of my text gives an answer of 768* pi/7 however i dont seem to be getting this value

    please help
    method of washers ...

    V = \pi \int_0^2 8^2 - (x^3)^2 \, dx
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  3. #3
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    Im wondering why it is that you have 8^2 - (x^3)^2

    and also what would this look like if it were a method of shells,
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  4. #4
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    Quote Originally Posted by XyxFibonaccixyX View Post
    Im wondering why it is that you have 8^2 - (x^3)^2

    method of washers ...

    \textcolor{red}{V = \pi \int_a^b [R(x)]^2 - [r(x)]^2 \, dx}

    and also what would this look like if it were a method of shells

    \textcolor{red}{V = 2\pi \int_0^8  y \cdot \sqrt[3]{y} \, dy}
    ...
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