Question 4 (20 marks) (a) Verify that the vector field F = yi + (x+zcos y) ] +sin yk is irrotational, and find a scalar function f (x, y, z) for...

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Question 4 (20 marks)(a) Verify that the vector field F = yi + (x+zcos y) ] +sin yk is irrotational, and find ascalar function f (x, y, z) for which F = Vf .(15 marks)(b) From the result in (a), evaluate |F . dr along any path from (0, 0, 0) to (3, 2, 0),where F =xi + yj + zk is the position vector of a moving particle.(5 marks)Question 5 (30 marks)Compute the following integrals using suitable method.(a) ff xydx dy , where R is the region bounded by y=1, y=1+x, and y=3-x.R(10 marks)(b) SIT-19-x? -y?edx dy dz, where V is the region bounded above by a spherex?+y? +z? =9 and bounded below by a plane z=1.(c) ff (at + y?)ds , where S is the part of the surface z= 9-x-y lying inside the(10 marks)cylinder x2 +y? =1.(10 marks)