Book 3.6.1: Is the 'Monte Carlo basics' correct?

[LiuZengqiang]

In book3-6.1Returning to the Cornell Box: Remember Monte Carlo basics: ∫f(x)≈∑f(r)/p(r) ..., Shouldn't the correct formula be ∫f(x)≈(1/N)*∑f(r)/p(r)?

[LiuZengqiang]

Maybe the correct formula is ∫f(x)dx≈(1/N)*∑f(r)/p(r)?

[dimitry-ishenko]

This is definitely a typo. From the wikipedia artice on Monte Carlo integration the correct formula should be:

$$ \int f(x) dx \approx \frac 1 N \sum_{i=0}^{N-1} \frac {f(x_i)} {p(x_i)} $$

Related to #1534