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Math Help - Infinite Area

  1. #1
    Junior Member
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    Infinite Area

    If the region R = { (x,y) : x >= 1, 0 <= y <= (1/x) } is rotated about the x-axis, the volume of the resulting solid is finite. Show that the surface area is infinite. ( don't need to compute the integral )


    I know the shape is called gabriel's horn. I think i have it right, I have got the surface area to be S = 2pi (integral from a to b) sqrt(1 + f'(x)^2))dx. I'm not sure if this is right though. Can someone go through this and see if I have done it correctly?

    TIA!!!!
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  2. #2
    MHF Contributor
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    S.A.=\int_{a}^{b}2\pi x \sqrt{1+f'(x)^2}dx

    You just forgot an x. Seems right to me.
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