E33.4 Evaluate JIJ div FdV, where F(x, y, z) = (r²y, -ry²,-2) and E is the solid ball z² + y² +2² ≤ 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
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E33.4

E33.4 Evaluate
JIJ div F dV, where F(x, y, z) = (x²y, -ry², -2) and E is the solid ball z² + y² + 2² ≤ 1.
E33.5 (a) Sketch the curve C with parametric equations
r = cost, y = sint, z = sint, 0≤t≤ 2.
(b) Find fF.dr, where F = (2re², 22²e²y + 2yz,y²).
(c) Find G dr, where G = (rz,z¹,yz³).
Transcribed Image Text:E33.4 Evaluate JIJ div F dV, where F(x, y, z) = (x²y, -ry², -2) and E is the solid ball z² + y² + 2² ≤ 1. E33.5 (a) Sketch the curve C with parametric equations r = cost, y = sint, z = sint, 0≤t≤ 2. (b) Find fF.dr, where F = (2re², 22²e²y + 2yz,y²). (c) Find G dr, where G = (rz,z¹,yz³).
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