Changing Variables in Multiple Integrals
Method 1 Eliminate x and y from the three simultaneous equations u = u(x, y), v = v(x, y), and the xy-equation of the boundary curve. For the x-axis and x = 1, this gives u = x + y u = x + y ˆ u = 1+y v = x −y ⇒ u = v; v = x −y ⇒ v= ⇒ u + v = 2. y = 0 x = 1 1−y Method 2 Solve for x and y in terms of u, v; then substitute x = x(u, v ... ................
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