Whence evaluating the area under the curve(adsbygoogle = window.adsbygoogle || []).push({});

[tex]y=\frac{1}{x} \\\ \mbox{for} \\\ 1 \leq x < \infty [/tex]

it evaluates to [tex]\infty [/tex]

But when evaluating the volume using

[tex] Volume = \pi \int y^2 dx \\\ \mbox{on} \\\ a \leq x < b [/tex]

hence

[tex] Volume = \pi \int \frac{1}{x^2} \\dx [/tex]

hence

[tex] Volume = \pi [-\ \frac{1}{x}] \\\ \mbox{on} \\\ 1 \leq x < \infty [/tex]

hence

[tex] Volume = \pi [0 - - 1] = \pi [/tex]

A finite value!

Im having trouble comprehending such concepts and ideas.

Can someone please explain?

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# Infinte Area but finite Volume

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