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241w-f13_15.5, 15.7-15.9

8 triple integrals in cylindrical coordinates

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Unformatted text preview: d the 3. Find the volume of the solid bounded by 9 15.8 Triple integrals in cylindrical coordinates cylindrical coordinates: Suppose a region E in space is described by Then ∭ ∫∫ ∫ 10 Example Find the volume and the moment of a inertia of a circular cone E of height H and radius R, and with constant density , about its center axis. 11 15.9 Triple integral in spherical coordinates The spherical coordinates related by and rectangular coordinates are ( When we evaluate triple integrals as repeated integrals in spherical coordinates, we need to multiply the integrant by a factor of 12 Examples 1. Find the volume and . (assuming density=1) of the ball 13 2. Let E be the region between and , in the first octant. Compute ∭ 14 . 3. Suppose E is the solid bounded below by and √ above by . Find its volume and its centroid. 15...
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