Example 8.1.1
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is the tetrahedron bounded by the planes , , , .
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Example 8.1.2
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is the tetrahedron cut from the first octant by the plane .
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Example 8.1.3
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is the region interior to the cylinder that is bounded below by the -plane, and above by the paraboloid .
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Example 8.1.4
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is the first-octant region bounded by the planes , and .
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Example 8.1.5
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is the wedge the planes and cut from the cylinder .
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Example 8.1.6
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is the first-octant region bounded above by the cylinder and on the right by the paraboloid .
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Example 8.1.7
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is the region enclosed by the cylinder and the planes and .
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Example 8.1.8
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is the region common to the two cylinders and .
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Example 8.1.9
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is the region enclosed by the cylinders and , and the planes and .
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Example 8.1.10
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is the region that is inside the cylinder , and that is bounded above and below by the planes , and , respectively.
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Example 8.1.11
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is the region bounded by the elliptic paraboloids and .
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Example 8.1.12
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is the region in the upper half-plane that is above the cone but below the sphere . (Use cylindrical coordinates.)
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Example 8.1.13
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is the region in the upper half-plane that is above the cone but below the sphere . (Use spherical coordinates.)
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Example 8.1.14
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If are the variables in spherical coordinates, is the region bounded inside by the surface and outside by the sphere .
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Example 8.1.15
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is the region inside the cylinder and between the planes and .
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Example 8.1.16
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is the region that lies inside the sphere , and is between the cones and .
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Example 8.1.17
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is the region that is bounded above by the paraboloid , below by the plane , and that lies outside the cylinder .
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Example 8.1.18
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is the region bounded below by the paraboloid and above by .
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Example 8.1.19
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is the first-octant region that lies between the cylinders and , and that is bounded below by the plane and above, by the surface .
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Example 8.1.20
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is the region that lies between the plane and the paraboloid .
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Example 8.1.21
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is the region enclosed by the surface , where are the variables in spherical coordinates.
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Example 8.1.22
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is the region that lies between the paraboloids and .
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Example 8.1.23
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is the region that lies inside both the sphere and the cylinder .
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Example 8.1.24
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is the region bounded above by the surface , and below by the surface .
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Example 8.1.25
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is the region bounded above by the sphere , and below by the paraboloid .
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Example 8.1.26
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is the region interior to the surface , where are the variables of spherical coordinates.
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Example 8.1.27
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is the first-octant region enclosed by the cylinder and the plane .
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Example 8.1.28
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is the region bounded by the paraboloid and the plane .
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Example 8.1.29
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is the first-octant region that is bounded by the coordinate planes, and the additional planes , .
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Example 8.1.30
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is the region common to the three cylinders , , .
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