Question

Let D be the plane region defined by the inequalities x >=1, 0<=y<=5x. Determine whether the improper integral I=int int[D]x^-3 e^(-y/x) dx dy converges or not, and find its value if it does.

Answer 1

\[inequalities: \ x \ge1,\ 0 \le y \le5x\]
\[I=\int\limits_{ }^{}\int\limits_{D}^{}x ^{-3}e ^{-y/x} \ dx \ dy\]