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Monte Carlo Integration of Multidimensional Integrals

As an example, consider the following six-dimensional integral \begin{equation*} \int_{-\infty}^{\infty}\mathbf{dxdy}g(\mathbf{x, y}), \end{equation*} where \begin{equation*} g(\mathbf{x, y})=\exp{(-\mathbf{x}^2-\mathbf{y}^2)}(\mathbf{x}-\mathbf{y})^2 \end{equation*} with d=6 .