Like our book, hey, I remember that question. Because the premise of using Green's formula is that the function has a first-order continuous partial derivative in the area D surrounded by L (I can't remember the specific reason, but you should learn mathematical analysis if you want to study it in depth), because the example contains 1/(x2+y2), so the function is discontinuous at (0,0). In order to meet the premise of Green's formula, it can be modified. However, for the accuracy of the results, the difference before and after the transformation must be small, so take an infinitesimal area and "dig it out" (0,0). It is worth mentioning that the circular curve "digging" is chosen in the example only because it can be simply calculated in the later curve integral. In fact, we can use other curves in other topics. I hope it will be helpful to you and I hope it will be adopted.