241w-f13_15.5, 15.7-15.9

8 triple integrals in cylindrical coordinates

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online