under what condition,can the integration $$\int_{\Delta}f(x_1,x_2,\dots,x_n)dx_1dx_2\dots dx_n, \text{where } \Delta \text{ is integration domain defined by function},f(x_1,x_2,\dots,x_n) \text{ is the integrated function }$$ be numerically computable?
I think the sufficient and necessary condition must depend on $\Delta$ and $f(x_1,x_2,\dots,x_n)dx_1dx_2\dots dx_n$.When $f(x_1,x_2,\dots,x_n)dx_1dx_2\dots dx_n$ is integratable, the condition must depend on the function that determine the domain $\Delta$. So the question may restated as :what kind of the two function makes the integration numerically computable? It seems to be easy, when know the integration is Lebsegue or Riemann integration.