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Math Help - Volume of a solid

  1. #1
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    Volume of a solid

    <br />
y= \frac {1}{x^5}~<br />
y=0~<br />
x=4~<br />
x=6~<br />

    Rotated about the y-axis.

    I keep coming up with:
    <br />
\frac {1}{9*6^9} - \frac {1}{9*4^9}<br />

    I don't know what I am doing wrong. pi*r^2 right (which would be pi*(1/x^5)^2)? So it should just be the integral of:

    <br />
\int_4^6 \frac {1}{x^{10}}~dx <br />

    Right?
    Last edited by redman223; September 25th 2008 at 03:44 PM.
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  2. #2
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    rotation is about the y-axis, so, using cylindrical shells ...

    V = 2\pi \int_4^6 \frac{1}{x^4} \, dx
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  3. #3
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    Could you explain those steps? I have trouble when the y-axis is involved.

    Where did the 2pi and the x^4 come from?
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  4. #4
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    are you familiar with using the method of cylindrical shells?
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  5. #5
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    I am, but I am used to rotating it about the x-axis or y=something other than zero. So rotating it about x=something other than zero or the y-axis throws a wrench into my methods.

    Normally I would just use the curve of the line as the radius and in the pi*r^2 equation right? Then subtract the smaller volume from the larger one and take the integral of that area right?
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  6. #6
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    you are thinking of washers ... not cylindrical shells.

    I recommend you research the method.
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