## anonymous 5 years ago Is it possible for an unbounded region to have a finite area? Can you give me examples.

1. anonymous

Of course just think about the graph of the function y=1/x^2 from x=1 to infinity. The area below the graph is $\int\limits_1^\infty \frac{1}{x^2}\textrm{d}x=[-1/x]_1^\infty=1.$ So it has a finite area but it' not bounded. See the attached picture:

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