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I am having a problem with change of variables problems in GENERAL. What I don't understand at this point is how one determines what the lower and upper bounds are in terms of the transformation variables. That is, if you have some wierd shaped region that can't be evaluated as either a type I or type II double integral. However, you'd still want to make sure to integrate from lower values of X to higher values of X right? How do you figure that out (by the way, I do realize that many textbooks draw arrows on the curves that make up the regions of integration. I have no idea what purpose these arrows serve.)