Question

is it possible for an unbounded region to have a finite area? Can you give me examples.

Answer 1

I am not sure about this but I believe the answer is yes. I believe example is Gabriels' Horn. If I remember correctly, Gabriel's Horn has an infinety region and yet it also has a finite area. Be advised, I am not positive about this answer.

Answer 2

\[I=\int\limits_{-\infty}^{+\infty}e ^{-x^2}dx = \sqrt{\pi}\]

Bell-Shaped Curve. This calculation involves improper integral, double integral, and changing variables to polar coordinates (Calc II & III materials)