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I find the slide a little bit confusing, especially with the different occurrence of f(x). It was helpful for me to think of it this way:

our goal is to calculate $$ I=\int f(x)dx $$ We can rewrite this as $$ I=\int {f(x)\over p(x)}p(x)dx $$ which is $E[{f(x)\over p(x)}]$.

By the derivation of the next slide, we can estimate this with ${1\over N}\sum {f(x_i)\over p(x_i)}$, where $x_i$~$p(x)$


That's good feedback. In retrospect I think that what you're suggesting--basically starting with the derivation we used later in the lecture, would make the ideas clearer. (The students next year can benefit from this!)