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Math Help - Torricelli's trumpet

  1. #1
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    Torricelli's trumpet

    Consider x>=0 and 0<=y<=1/x.

    Show that this has finite volume.

    I get integral from 0 to infinity of 2pi*(1/x^2), but this does not converge because of the asymptote, right? I know it would converge, and so have finite volume, if I took 1 to infinity. On the other hand, when I do 0 to infinity, it diverges, right? Is this probably a typo on my sheet or am I doing something wrong
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  2. #2
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    Quote Originally Posted by twittytwitter View Post
    Consider x>=0 and 0<=y<=1/x.

    Show that this has finite volume.
    You have a mistake in definition.
    See this.
    It should be x\ge 1.
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