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Tackling the Volume Integral

  1. Dec 21, 2012 #1
    Can I calculate the volume of any function rotated once about the y-axis by multiplying the definite integral of that function by 2*pi*r?

    For example if we want to generate a solid 3d shape from the function -x^2+1 we multiply the integral of it, (x - x^3 / 3), by 2*pi*1. The reason r is one in this case is because the points where the function crosses the x axis are 1 unit away from the y axis: (-1,0) and (1,0.)

    (I have not taken a calculus class yet, this is just my personal reasoning.)
     
  2. jcsd
  3. Dec 22, 2012 #2

    SteamKing

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    Check out the Theorem of Pappus.
     
  4. Dec 22, 2012 #3
    Thanks. It also turns out that r in 2*pi*r is just the size of the closed interval in the integral. So in theory this should work for any definite integral.
     
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