Thanks for the tip but all I get is 0 for the integral.  Any other
suggestions?

int <- function(y){
u2 = y[1]
z2 = y[2]
u1 =y[3]
z1 = y[4]

reg.nonzero <- (u2 > z1 & u2 < z2) & (z2 > z1 & z2 < 12) & (u1 > 4 & u1 <
z1) & (z1 > 4 & z1 < 12)


ff <- ifelse (reg.nonzero, u1*(z1-u1)*u2*(z2-u2)*exp(-0.027*(12-z2)), 0)


return(ff)


}


cuhre(4,1,int)

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