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I @ 茧 ދn S I g @TEL F @ @. C C′ This looks reasonable purely formally, since we get the right side by substituting into the left side the expressions for z and dz in terms of x and y z = f(x, y), dz = fxdx fydy To justify it more carefully, we use the parametrizations given above for C and C′ to calculate the line integrals t1 dz P (x, y, z)dz = P (x(t),y(t),z(t.