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Depending on the function f(x,y) or the region R changing from cartesian to polar coordinates might make our lives easier.
If we change variables from (x,y) to polar coordinates, (r,θ) , we need to relate the variables x and y to the new variables, and need to relate the area element dxdy to the area element drdθ . In the following, we'll do this specifically for polar coordinates (r,θ) , and in general assuming that we're using some arbitrary coordinates (u,v) . For polar coordinates, the relationship between x , y , r , and θ is
