(a) Sketch the domain of integration for the double integral VI-y 1 = 1 /1/0 I...

   

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(a) Sketch the domain of integration for the double integral VI-y 1 = 1 /1/0 I 1-y (2 + y)drdy. Reverse the order of integration, to express I in terms of a double integral in which the inner integration is with respect to y and hence evaluate I. (b) For the vector field F(r) = (-ry, ry, yz) evaluate the line integral [F(r). dr where r is the position vector and C is the curve y = 1 - 2 for z = 0 and 0 x1. (c) For the vector field F(r) defined in part (b), evaluate e curl F where e3 is the basis unit vector in the direction of the z-axis and comment on a theorem that connects your answers to parts (a) and (b). Hence, without further integration, write down the value of the line integral Jo F(r) - dr along the curve C" given by y = 1 - for z = 0 and 0 x 1. a (a) Sketch the domain of integration for the double integral VI-y 1 = 1 /1/0 I 1-y (2 + y)drdy. Reverse the order of integration, to express I in terms of a double integral in which the inner integration is with respect to y and hence evaluate I. (b) For the vector field F(r) = (-ry, ry, yz) evaluate the line integral [F(r). dr where r is the position vector and C is the curve y = 1 - 2 for z = 0 and 0 x1. (c) For the vector field F(r) defined in part (b), evaluate e curl F where e3 is the basis unit vector in the direction of the z-axis and comment on a theorem that connects your answers to parts (a) and (b). Hence, without further integration, write down the value of the line integral Jo F(r) - dr along the curve C" given by y = 1 - for z = 0 and 0 x 1. a

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a To sketch the domain of integration note that 0 leq y leq 1 and 1y leq x le... View the full answer