Clarification of "change of variables" for multiple integration This isn't really a question about a specific math problem, but rather for the change of variables of multiple integration as a whole. When you change variables you have to multiply the new expression by the jacobian of the new functions you chose. So, if the determinant is a positive constant, you can just bring it outside of the integral signs. However, in my book, whenever the determinant is a negative constant, they bring out its positive reciprocal instead (For example, if the jacobian determinant is -1/3, they bring out a 3 instead) Is this the proper way to do it? For example, there is q eustion where you use the substituion u = x+y, v = x-y the determinant of this is -2 ( ad - bc = -1 - 1 = 2), so in the solutions in the back of the book they've turned they've multiplied the new expression by 1/2 instead of by -2 Is this the rule? If determinant is a positive constant, you use that constant, and if it's a negative one, you use its positive reciprocal?