01:640:251 Lecture Notes - Lecture 17: Spherical Coordinate System

• School: Rutgers University
• Department: Mathematics
• Course: 01:640:251
• Professor: Guadagni

Document Summary

Section 15. 4: integration in polar, cylindrical and spherical coordinates. Triple integrals rectangular: = cylindrical: = spherical: = +sin () Let d be the region given by + + + 2, 1 in the xy-plane. Since we are using polar coordinates we will use = Slice region d with a curve of constant q. Line: = 1 = 1 = : Circle: + ++ = 2 + = 2 = 2. From the shape of region d we find that 2 = p. Let w be the region inside the sphere + ++ ++ = 9 and outside the cylinder + + + = 4. Calculate c using (;<=><=a