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Thread: Finding volume by rotating the region bounded by the given curves

  1. March 9th 2011, 05:03 AM #1
    softballchick
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    Finding volume by rotating the region bounded by the given curves

    Find the volume of the solid obtained by rotating the region (in both the first and second quadrants) bounded by the given curves about the specified axis.
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    I got but seems to be wrong...
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  2. March 9th 2011, 05:15 AM #2
    TheChaz
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    This is how I would set it up...

    V = \pi * \int_{-1}^{1}(6 - x^2)^2dx - \pi*\int_{-1}^{1}(6 - 1)^2dx

    This is basically integrating the area of a cross-section, which has A = \pi r^2. Then we see that the "radii" are given by (6 - f(x)) and (6 - g(x))
    Where f and g are the given functions x^2 and 1.
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