Task 3: Triple Integral - Cylindrical Coordinate. A solid region E lies within the paraboloid x=3-y2-z2,...

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Task 3: Triple Integral - Cylindrical Coordinate. A solid region E lies within the paraboloid x=3-y2-z2, cylinder y+z2 =1, and the plane 2x+y=1. a) Draw the diagram using the mathematical application (GeoGebra etc.) (3 marks) b) Draw the projection of the diagram using the mathematical application (from view x, y, and z) (GeoGebra etc.) (3 marks) c) Hence, evaluate 3xdV using an appropriate coordinate system. (8 marks) Task 3: Triple Integral - Cylindrical Coordinate. A solid region E lies within the paraboloid x=3-y2-z2, cylinder y+z2 =1, and the plane 2x+y=1. a) Draw the diagram using the mathematical application (GeoGebra etc.) (3 marks) b) Draw the projection of the diagram using the mathematical application (from view x, y, and z) (GeoGebra etc.) (3 marks) c) Hence, evaluate 3xdV using an appropriate coordinate system. (8 marks)