Claim: Substitution may be used to integrate functions of several variables and to express the fact that the absolute value, or the non-negative value of x, may be equal to the volume.
Evidence: In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. One may also use substitution when integrating functions of several variables. This formula expresses the fact that the absolute value of the determinant of a matrix equals the volume of the parallelotope spanned by its columns or rows.