When we deal with multidimensional integrals of the form $$ \begin{equation*} I=\int_{a_1}^{b_1}dx_1\int_{a_2}^{b_2}dx_2\dots \int_{a_d}^{b_d}dx_d g(x_1,\dots,x_d), \end{equation*} $$ with \( x_i \) defined in the interval \( [a_i,b_i] \) we would typically need a transformation of variables of the form $$ \begin{equation*} x_i=a_i+(b_i-a_i)t_i, \end{equation*} $$ if we were to use the uniform distribution on the interval \( [0,1] \).