I'm doing a project that involves numerical method, but I'm not too familiar on calculus.
I'm using Simpson's rule to integrate n-dimension gaussian, I was able to get the integration result for n-dimension, but how do I get the error rate?
For 1-D, according to Wiki, it's simply $$ \frac{1}{90} (b-a)^5 f''''(k) $$
So, for 1-D, I can get $$ f(x) = e^{-x^2} $$ $$ f''''(x) = 4(4x^4-12x^2+3) e^{-x^2} $$
But how do I do this for example for 2-D? $$ \int_{a}^{b} \int_{c}^{d} e^{-(x^2 + y^2)} dx dy $$
Thanks a lot for the help.
