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Math Help - Volume by revolution

  1. #1
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    Volume by revolution

    Let S be the region in the first quadrant bounded by the graphs of y = x^1 ^/ ^5 and y = x^2 Region S is the base of a solid whose cross sections perpendicular to the x-axis are squares. Find the volume of the solid.
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  2. #2
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    Quote Originally Posted by Cursed View Post
    Let S be the region in the first quadrant bounded by the graphs of y = x^1 ^/ ^5 and y = x^2 Region S is the base of a solid whose cross sections perpendicular to the x-axis are squares. Find the volume of the solid.
    Which is the axis of revolution?
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  3. #3
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    This is not a revolution problem. The cross sections are perp. to the x-axis, so it looks like we integrate wrt x by using the area of the squares.

    Since the cross-sections are perp. to the x-axis, then the squares will have base width y and area y^2.

    But y=x^{\frac{1}{5}}-x^{2}

    So, we need \int_{0}^{1}[x^{\frac{1}{5}}-x^{2}]^{2}dx
    Last edited by galactus; November 24th 2008 at 05:38 AM.
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