4. Suppose that 'Ij;(B) and ¢(E) are CP surfaces, and 'Ij; = ¢ 0 T, where T is a Cl function from B onto E.

(a) If ('Ij;, B) and (¢, E) are smooth, and T is 1-1 with AT > 0 on B, prove for all continuous F : ¢( E) -T R 3 that L F(¢(u, v)) . Nq,(u, v) d(u, v) = Is F('Ij;(s, t)) . N",(s, t) d(s, t).

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(b) Let Z be a closed subset of B of area zero, ('Ij;, B) be smooth off Z, and T be 1-1 with AT > 0 on BO \ Z. Prove for all continuous F : ¢(E) -T R3 that L F(¢(u, v)) . Nq,(u, v) d(u, v) = Is F('Ij;(s, t)) . N",(s, t) d(s, t).