1) Find the volume of the solid that lies between the paraboloid z = 2x2 + 2y2 and the plane z = 8. 2) Find the volume of the solid bounded by the cylinder x2 + y 16 and from z 1 to z + x = 2 %3D 3) Find the volume of the region bounded above by the paraboloid z 3 - x2 - y and below by the paraboloid z 2x2 + 2y.

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Part (4) Triple Integration in Cartesian coordinates:
1) Find the volume of the solid that lies between the paraboloid z = 2x2 + 2y and the plane
Z = 8.
2) Find the volume of the solid bounded by the cylinder x2 + y = 16 and from z = 1 to z + x
= 2
3) Find the volume of the region bounded above by the paraboloid z = 3 - x2 - y and below
by the paraboloid z 2x2 + 2y.
4) Find the volume of the region in the first octant bounded by the coordinate planes, the
plane x + y = 4, and the cylinder y + 4z? = 16
Transcribed Image Text:Part (4) Triple Integration in Cartesian coordinates: 1) Find the volume of the solid that lies between the paraboloid z = 2x2 + 2y and the plane Z = 8. 2) Find the volume of the solid bounded by the cylinder x2 + y = 16 and from z = 1 to z + x = 2 3) Find the volume of the region bounded above by the paraboloid z = 3 - x2 - y and below by the paraboloid z 2x2 + 2y. 4) Find the volume of the region in the first octant bounded by the coordinate planes, the plane x + y = 4, and the cylinder y + 4z? = 16
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