So it's been a while since I've had to do any remotely difficult integration, and one of my profs kind of sprung this on us.
$ \int_{x=0.5}^{x=1.5}\int_{-0.5}^{0.5}\frac{dx\;dy}{\sqrt{x^2+y^2}} $
If I convert to polar coordinates and integrate, I get r times theta or: $ \sqrt{x^2+y^2}\cdot \tan^{-1}(\frac{y}{x}) $ In rectangular coordinates. However, whenever I tired using the limits given, I arrive at an answer of 0.0933, when the expected value is close to 1. Does anybody know what could have gone awry? I think the integration method is correct, but I'm not sure.