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[quote]Find where the path is the boundary of the triangle given by x = 0, y = 0, and x + y = 1,[\quote]
First we need to define our area of integration. This is a right triangle with verticies at (0, 0), (1, 0), and (0, 1).
I will write
Green's theorem says that
So we first find :
Now, the area of this region is in the direction so: