If f(x) = x to a power between -0.5 and -1, the area between the f(x) graph and the x-axis from, say x=1 to infinity is infinite, but the volume of revolution of f(x) around the x-axis is finite. This seems counter-intuitive. Can anyone give a satisfying explanation of this - preferably a geometrical one please - not just the algebraic integration please - as I'm struggling with this idea.(adsbygoogle = window.adsbygoogle || []).push({});

Thanks, in anticipation.

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# Volume of revolution

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