I am trying to integrate this function:
$$a\int_{x=-R}^{x=+R}\int_{y=-\sqrt{R^2-x^2}}^{y=+\sqrt{R^2-x^2}} \exp\left(-\frac{1}{2}\left( \left(\frac{x}{b}\right)^2 + \left(\frac{y}{c}\right)^2\right)\right)\,dx \,dy$$
However, Wolfram Alpha tells me that there is no analytical expression.
What am I doing wrong?