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For on-topic question related to uses of the mathematical concept of an integral, i.e. $\int_a^b f(x)\; dx$. Purely mathematical questions about integrals are better asked at math SE: https://math.stackexchange.com/

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Monte Carlo Approximation on integral of Gaussian pdf on Convex Domain

I have hard time on estimating the following integral on convex domain ($\mathcal D$) using Monte-Carlo approximation. … Note that this integral might not have a closed-form since $\mathcal D$ can be, for example, intersection of three disks. …