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Math Help - Volume by Slicing help

  1. #1
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    Volume by Slicing help

    Find the volume of the solid that is generated when the region bounded by

    y = (x^2/16), y = 4, x = 0

    Revolved around

    y = -2

    Can somebody tell me where to start? I'm not sure. Do I use the formula:

    \int \pi (f(x)^2 - g(x)^2) dx

    In that case, what would be the g(x)? 0?

    So far I just know I'm integrating from 0 to 1.

    Thanks,

    John
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  2. #2
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    Quote Originally Posted by JohnM25 View Post
    Find the volume of the solid that is generated when the region bounded by

    y = (x^2/16), y = 4, x = 0

    Revolved around

    y = -2

    Can somebody tell me where to start? I'm not sure. Do I use the formula:

    \int \pi (f(x)^2 - g(x)^2) dx

    In that case, what would be the g(x)? 0?

    So far I just know I'm integrating from 0 to 1.

    Thanks,

    John
    first and most important step ... make a sketch of the region and the axis of rotation.

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

    V = \pi \int_{-8}^8 [4 - (-2)]^2 - \left[\dfrac{x^2}{16} - (-2)\right]^2 \, dx
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  3. #3
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    Quote Originally Posted by skeeter View Post
    first and most important step ... make a sketch of the region and the axis of rotation.

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

    V = \pi \int_{-8}^8 [4 - (-2)]^2 - \left[\dfrac{x^2}{16} - (-2)\right]^2 \, dx

    Thanks, this worked out, although I integrated from 0 to 8. Seeing a picture does infact help.

    John
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