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Math Help - More volume problems integration

  1. #1
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    More volume problems integration

    Am I on the right path for this first problem?
    Problem 1:
    Use Shell method, rotate about X axis
    Curve: x = 4y - y^2 - 3
    solving for y
    x + 3 = 4y - y^2
    x + 3 + y^2 = 4y
    (x + 3 + y^2)/4 = y

    Is this correct so far?

    Problem 2:
    use Disks, rotate about Y axis
    Curve: y = x^1/3
    formula for disks: pix^2 dy
    so we must solve for x
    I seem to be at a loss for how to get something = x
    do we multiply both sides by a certain exponent to get an exponent of x^1?

    any tips, thanks
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  2. #2
    MHF Contributor

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    Re: More volume problems integration

    Quote Originally Posted by togo View Post
    Am I on the right path for this first problem?
    Problem 1:
    Use Shell method, rotate about X axis
    Curve: x = 4y - y^2 - 3
    solving for y
    x + 3 = 4y - y^2
    x + 3 + y^2 = 4y
    (x + 3 + y^2)/4 = y

    Is this correct so far?
    No, it isn't, because you haven't yet "solved for y" with that "y^2" on the left.

    Problem 2:
    use Disks, rotate about Y axis
    Curve: y = x^1/3
    formula for disks: pix^2 dy
    so we must solve for x
    I seem to be at a loss for how to get something = x
    do we multiply both sides by a certain exponent to get an exponent of x^1?
    A 1/3 power is the cube root, isn't it? And the opposite of the cube root is cubing.

    any tips, thanks
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