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Suppose I am given a problem where I have to change the order of a function f(x,y) with some limits. Then I can successfully draw the all the limits, as well as find the region of integration. The problem, however, comes when I have to 'split' the region of integration. I am unable to understand when am I supposed to divide the region and how. I have lots of problems in which the region has to be divided to get the correct answer.

Assuming I get past dividing the region, I dont understand how do I change the limits of integration. If the original function is f(x,y)dxdy, then when the order is changed it will be f(x,y)dydx and the outer limits ( x in this case) will remain constant. But I am unable to get the limits for the 'inner' part(i.e y). I tried reading through the various other threads all over the Internet, but I end up getting even more confused.

Help will be highly appreciated.

Thanks in advance.