3. Evaluate the following integrals: (a) falz| dz, where C is an arc of unit circle...

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3. Evaluate the following integrals: (a) falz|² dz, where C is an arc of unit circle |2| = 1 traversed in the clockwise direction with initial point –1 and final point i. (b) Sa]z|zdz, where C consists of the half-circle z = segment: - R< Re z < R, Im z = 0 and traversed in the anticlockwise direction. Ans: RTi Ret, 0<t < T, and the straight line (c) Sazdz, where C consists of the semi circle z segment: z = it, – 1<t< 1, and traversed in the anticlockwise direction. = et, – <t <, and the straight line Ans: Ti 4. Explain why the integrals in question 3 cannot be evaluated by the method of indefinite integral. 3. Evaluate the following integrals: (a) falz|² dz, where C is an arc of unit circle |2| = 1 traversed in the clockwise direction with initial point –1 and final point i. (b) Sa]z|zdz, where C consists of the half-circle z = segment: - R< Re z < R, Im z = 0 and traversed in the anticlockwise direction. Ans: RTi Ret, 0<t < T, and the straight line (c) Sazdz, where C consists of the semi circle z segment: z = it, – 1<t< 1, and traversed in the anticlockwise direction. = et, – <t <, and the straight line Ans: Ti 4. Explain why the integrals in question 3 cannot be evaluated by the method of indefinite integral.