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Math Help - Volume of revolution

  1. #1
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    Volume of revolution

    If anyone can help me with this, I'd really appreciate it. Thanks!

    Find the volume of the solid generated by revolving the region bounded by the lines and curves about the x-axis.
    1. y = x^2 , y= 0 , x = 2
    2. y = x , y = 1 , x = 0
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  2. #2
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    1. <br />
\pi \int\limits_0^2 {\left[ {(x^2 )^2  - 0^2 } \right]} {\rm  }dx = \pi \int\limits_0^2 {x^4 dx = } \pi \left. {\left[ {\frac{1}{5}x^5 } \right]} \right|_0^2  = \frac{{32}}{5}\pi <br />
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  3. #3
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    2. <br />
\pi \int\limits_0^1 {\left[ {(1)^2  - x^2 } \right]} {\rm  }dx = \pi \int\limits_0^1 {(1 - x^2 )dx = } \pi \left. {\left[ {x - \frac{1}{3}x^3 } \right]} \right|_0^1  = \frac{2}{3}\pi <br />
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