1. The problem is to evaluate an integral by converting to polar coordinates. 2. When converting to polar coordinates, we use the transformations $x = r\cos\theta$ and $y = r\sin\theta$. 3. The area element $dx\,dy$ becomes $r\,dr\,d\theta$ in polar coordinates. 4. The limits of integration must be adjusted according to the region described in the problem. 5. Substitute the expressions for $x$, $y$, and $dx\,dy$ into the integral. 6. Evaluate the resulting integral over $r$ and $\theta$. Since the exact integral or region is not specified, please provide the integral or region to proceed with the evaluation.