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cuhre usage ?? multidimensional integration

I'm not quite familiar with R. Could you recommend some relative material.

Actually, I'm not intend to loop from 1 to 1. I'm just trying to see if it
works. It's supposed to be some len>1.

I'm trying to solve the following example: 

there are 3 types of variables(x,w,t), they are not independent and have
different distribution. 
Within each type, there are more than 1 variables. I need to integrate all
the variable.

joint pdf is like f(x,w,t)=?_i??f1(wi)f2(ti)?(?_j??f3(xj)
?_j??f4(xj*wi-ti?)?)


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