Question 3 Let F ( x , 8 , 2 ) = cyit ( * + 2 cosy ) ] + siny K , where c is a real constant . ( a ) Find the value of c such that F is irrotational...

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Question 3Let F ( x , 8 , 2 ) = cyit ( * + 2 cosy ) ] + siny K , where c is a real constant .( a ) Find the value of c such that F is irrotational .*( 5 marks )( b ) With the value of c obtained in ( a ) , determine a potential function ( ( xx , Y , 2) such that*VIP = F ." ( 10 marks )( C ) With the value of c obtained in ( a ) , evaluate { { . di , where C is the path movingfrom a point ( 0 , 0, 0 ) to ( 1 , IT / 2, IT / 2) along a straight line .( 5 marks)Question 4Compute the following integrals using suitable methods .( 2 ) JJS ( * 2 + y 2 ) as , where S is the part of the surface 2 = 9 - 2 x - y lying inside the cylinder : "* 2 + 12 = 1 .( 15 marks )( 6 ) JSE F . Kids , where { = xt't Y ] + z k and S' is boundary surface of the region boundedby the cone z = 3 ( * 2 + 1 2 ) and the upper half sphere * 2 + y 2 + 2 2 = 8 ( here n is theoutward - pointing normal ) .( 15 marks )- END -