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Math Help - Volume by Slicing - # 2

  1. #1
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    Volume by Slicing - # 2

    The solid lies between planes perpendicular to the x axis at x = -1 and x = 1. The cross-sections perpendicular to the x axis between these planes are squares whose bases run from the semi-circle y = -\sqrt{1 - x^{2}} to the semi-circle y = \sqrt{1 - x^{2}}
    V = \int_{a}^{b} A(x) dx

    x^{2} is the area of a square

    A = x^{2}

    V = \int_{-1}^{1} [2 \sqrt{1 - x^{2}}]^{2} On the right track here?

    V = \int_{-1}^{1} [4 (1 - x^{2})]

    V = \int_{-1}^{1} 4 - 4x^{2}

    The book says the answer will come out to \dfrac{16}{3}
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    Re: Volume by Slicing - # 2

    Are you supposed to rotate this region about an axis? As it is, you have described a 2 dimensional region, so there is no volume...
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    Re: Volume by Slicing - # 2

    Same idea as your other thread Volume by Slicing.

    - Hollywood
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    Re: Volume by Slicing - # 2

    The solid lies between planes perpendicular to the x axis at x = -1 and x = 1. The cross-sections perpendicular to the x axis between these planes are squares whose bases run from the semi-circle y = -\sqrt{1 - x^{2}} to the semi-circle y = \sqrt{1 - x^{2}}
    V = \int_{a}^{b} A(x) dx

    x^{2} is the area of a square

    A = x^{2}

    V = \int_{-1}^{1} [x][2 \sqrt{1 - x^{2}}]^{2} dx

    V = \int_{-1}^{1} [x][4 (1 - x^{2})] dx

    V = \int_{-1}^{1} [x][4 - 4x^{2})] dx

    V = \int_{-1}^{1} 4x - 4x^{2})] dx

    V = \dfrac{4x^{2}}{2}- \dfrac{4x^{3}}{3})]

    V = 2x^{2} - \dfrac{4x^{3}}{3})]
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