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Math Help - Volumes of a solid of revolutions

  1. #1
    Member Awsom Guy's Avatar
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    Volumes of a solid of revolutions

    Hello,
    This question I am having trouble with.
    Question:
    Find the volume of the solid generated when the curve y=x^(1/3) is rotaded about.
    (i) about the x-axis.

    My attempt:
    Intergrated = x^(10/3)
    pi(8)^(10/3)
    =1024pi
    =3216.991
    I am not sure if the answer because I think it's wrong.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    Hello,
    This question I am having trouble with.
    Question:
    Find the volume of the solid generated when the curve y=x^(1/3) is rotaded about.
    (i) about the x-axis.

    My attempt:
    Intergrated = x^(10/3)
    pi(8)^(10/3)
    =1024pi
    =3216.991
    I am not sure if the answer because I think it's wrong.
    What are your limits of integration?
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  3. #3
    Member Awsom Guy's Avatar
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    oops sorry, 8 and 0.
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    oops sorry, 8 and 0.
    So, by discs we have V=\pi\int_0^8[x^{1/3}]^2dx
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  5. #5
    Member Awsom Guy's Avatar
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    umm.. [x^(1/3)]^2, because of the volume thing.
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Note the edit
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  7. #7
    Member Awsom Guy's Avatar
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    yes I did that so... continue please
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  8. #8
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    yes I did that so... continue please
    Evaluate \frac{3}{5}x^{5/3}\Big|_0^8
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  9. #9
    Member Awsom Guy's Avatar
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    I see my mistake thanks...
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  10. #10
    Member Awsom Guy's Avatar
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    how did you get 5. on the denominator.
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  11. #11
    Member Awsom Guy's Avatar
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    how is it power of 5/3 I think it should be 10/3.
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  12. #12
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    how did you get 5. on the denominator.
    By the power rule for integration:

    \int{x^{2/3}}dx=\frac{x^{5/3}}{5/3}+C=\frac{3}{5}x^{5/3}+C
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  13. #13
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by awsom guy View Post
    how is it power of 5/3 i think it should be 10/3.
    2/3+1=5/3
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  14. #14
    Member Awsom Guy's Avatar
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    are you sure it isn't:
    x^(1/3)^2
    = x^(10/3).
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  15. #15
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    are you sure it isn't:
    x^(1/3)^2
    = x^(10/3).
    Yes, I'm sure.

    [x^{1/3}]^2=x^{2/3}
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