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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
∫∫ ∫ 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
, 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
. Find its volume and its centroid. 15...
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This note was uploaded on 01/31/2014 for the course EAS 207 taught by Professor Richards during the Fall '08 term at SUNY Buffalo.
- Fall '08