Question: Consider the vector field F~ = (4xy z)~i 8x~j + ~k, the half-plane 2x + y = 2, (z 0) and o piece of paraboloid

Consider the vector field F~ = (4xy z)~i 8x~j + ~k, the half-plane 2x + y = 2, (z 0) and o piece of paraboloid z = 4 y- 4x , (z 0). a)Parameterize the curve C determined by the intersection of the flat surface and the paraboloid. b) Calculate the flux of the rotational of the field F~ over the portion of the semiplane bounded by C. c)Calculate the flux of the rotational of the field F~ over the portion of the semiplane bounded by C. d) What relationship exists between these two integrals? Justify

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