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Volume of revolution and areas

  1. Mar 17, 2010 #1
    I'm having a bit of trouble when it comes to volume of revolutions and areas. I find it quite difficult when it comes to setting up the integral. Could someone explain to me or give me a tutorial on how to set up the equations thanks!

    Here are a few examples

    The region enclosed by the curves y = x^2 and x = y^2 is rotated about the line y = -2. Find the volume of the resulting solid.

    Find the volume of the solid formed by rotating the region enclosed by the curves y=e^(x) + 2, y=0 , x=0, and x=0.1 about the x-axis.

    Find the volume of the solid obtained by rotating the region enclosed by the curves y=x^2 and x = y^2 about the line x=-1.

    The region enclosed by the curves x = 1 - y^4 and x = 0 is rotated about the line x = 4. Find the volume of the resulting solid.

    Thanks for all the help!
     
  2. jcsd
  3. Jul 26, 2010 #2
    Hi,
    Volume and area questions are relatively simple once you come to terms with whats actually going on. I have been working on some tutorials for volume and area problems on my science community website (although it's still very young in development). We plan on developing a very extensive tutorial database but it's going to be a long process.
    Click http://www.theoremsociety.com/forums/index.php?showforum=7" [Broken] for the tutorials page.
    Also I would check out homework problems that have been asked here. Volume questions seem to reappear quite often on PF.
     
    Last edited by a moderator: May 4, 2017
  4. Jul 26, 2010 #3
    For the method of rings/disks:
    Rotation over vertical line in form of x = f(y)
    Rotation over horizontal line in form of y = f(x)
    Formula: pi*((outer radius)2 - (inner radius)2)

    For the method of cylinders/shells:
    Rotation over vertical line in form of y = f(x)
    Rotation over horizontal line in for of x = f(y)
    Formula: pi*radius*height

    Remember to draw diagrams. Keep in mind, when you're given a restriction for x = _ that's a vertical line, and y = _ is a horizontal line.
     
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