Use the method of this example to calculate F · dr, C where F(x, y) = 2xyi + (y2 − x2)j (x2 + y2)2 and C is any positively orien
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The transformation is a reflection in the line 
followed by a reflection in the line 
.
The mapping for a reflection in the line is 
.
That is simply swapping the coordinates.
Now we reflect the resulting coordinates in the line which has the mapping 
So we transform the resulting coordinates as follows:
Hence we have
The mapping for a reflection in the line
That is simply swapping the coordinates.
Now we reflect the resulting coordinates in the line
So we transform the resulting coordinates as follows:
Hence we have