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 $[0,1]$.