Can an Unbounded Region Have Finite Area? - Expii

For example, does the (infinitely tall) region \(0\le y\le 1/x^2, 0\le x\le 2\) have finite or infinite area? How about the (infinitely wide) region \(0\le y\le 1/x^2, 2017\le x<\infty\)? Just as definite integrals represent areas of bounded regions, the improper integrals we'll consider next are supposed to represent areas of unbounded regions.