Let $C$ be a circle of unit area with centre at origin and let $S$ be a square of unit area with $(1/2,1/2)$,$(-1/2,1/2)$,$(1/2,-1/2)$ and $(-1/2,-1/2)$ as the four vertices. If $X$ and $Y$ be two independent standard normal variate, show that $$\int \int_{C} \phi(x)\phi(y)dxdy \geq \int \int_{S} \phi(x)\phi(y)dxdy$$ where $\phi()$ is the pdf of $N(0,1)$
Any ideas on how to do this?