a) Use double integrals to find the volume of the solid lying under the surface z = 1+x+y and above the region in the xy-plane bounded by x = y² and .x = 4. b) Find the mass of the region bounded by the curve r = 2 sin given that the density across the region is constant. c) An ice cream cone can be described as being a solid bounded below by the cone ==√√3(x² + y²) and above by the hemisphere .x² + y² +2²=1, z 20. The volume of such a cone (ice cream and cone combined) can be calculated using triple integrals. (i) Set up the triple integral in rectangular co-ordinates to calculate the volume. (ii) Set up this triple integral in cylindrical co-ordinates to calculate the volume. (iii) Set up this triple integral in spherical co-ordinates to calculate the volume. (It may be helpful to know that the cone makes an angle of with the z axis.) (iv)Calculate the volume of this ice cream cone.

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a) Use double integrals to find the volume of the solid lying under the surface z = 1+x+y and above the region in the xy-plane bounded by x = y² and .x = 4. b) Find the mass of the region bounded by the curve r = 2 sin given that the density across the region is constant. c) An ice cream cone can be described as bei