3. (i) Using the definition of the line integral of a vector field, calculate the line integral L3 F.dy of the vector field F: R2 → R2 given by F(x, y) = (y, x), and where the curve & is the unit semi-circle centred at the origin, located in the upper half-plane and oriented in the anticlockwise direction. Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9 in the Notes). [20 Marks] (ii) Calculate the same integral using Green's Theorem. [10 Marks]

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.