# Thread: Evaluation of improper double integrals

1. ## Evaluation of improper double integrals

How do I evaluate the improper double integral of 1/x-y dy dx where 0=<x<=1 and 0=<y<=x?

2. Originally Posted by vpapandr
How do I evaluate the improper double integral of 1/x-y dy dx where 0=<x<=1 and 0=<y<=x?
$\int_0^1\int_0^x\frac{dy}{x-y}dx$

This integral is divergent, to show this just show that

$\lim_{\varphi\to{x^-}}\int_0^{\varphi}\frac{dy}{x-y}$ diverges to infinity.