Question

Hi, I'm working on pset6 and have a question regarding 3C-4. 'The Solutions to integration problems' explain it is the infinite region between the curve y = x^−10 and the x-axis for x > 0. Shouldn't it be the region for x > 1?

Answer 1

Probably not, as the integral\[\int\limits_{1}^{\infty}x ^{-10}dx\]is finite whereas\[\lim_{t \rightarrow 0^{+}}\int\limits_{t}^{\infty}x ^{-10}dx\]is not.