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Math Help - Another Volume Problem

  1. #1
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    Another Volume Problem

    I would like to know if I have set this up correctly:

    Find the volume of a solid obtained by rotating the region bound by y = cos^2 (x) , -pi/2 < x < pi/2, y = 1/4 about the line x = pi/2.

    I came up with

    2 pi Integral from -pi/2 to 0 of (1+x)(cos^2x - pi/2)
    +
    2 pi Integral from 0 to pi/2 of (1-x)(cos^2x - pi/2)

    Does this seem OK?
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  2. #2
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    ever use the method of cylindrical shells?

    V = 2\pi \int_{-\frac{\pi}{3}}^{\frac{\pi}{3}} \left(\frac{\pi}{2} - x\right)\left(\cos^2{x} - \frac{1}{4}\right) \, dx
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  3. #3
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    I thought I was using shells!

    Dont I need two different integral since the radius changes from positive to negative?
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  4. #4
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    no ... the radius is r = \left(\frac{\pi}{2} - x\right) no matter what x is.

    think about the value of \left(\frac{\pi}{2} - x\right) for x > 0 and x < 0.
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  5. #5
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    OK, I think I understand. I don't really know what I was trying to do! Thanks a lot for helping.
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