Use the Divergence Theorem to calculate the surface integral fSs F · dS; that is, calculate the flux of F = 4x³z i + 4y³zj + 3z4 k F(x,y,z) = S is the sphere with radius R and center the origin.
Use the Divergence Theorem to calculate the surface integral fSs F · dS; that is, calculate the flux of F = 4x³z i + 4y³zj + 3z4 k F(x,y,z) = S is the sphere with radius R and center the origin.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Use the Divergence Theorem to calculate the surface integral fSs F · dS; that is, calculate the flux of F across S.
= 4x³z i + 4y³zj + 3z4 k
F(x,y,z) =
S is the sphere with radius R and center the origin.

Transcribed Image Text:Use Stokes' Theorem to evaluate SSs curl F· dS.
F(x,y,z) = x2z2 i + y²z² j + xyz k
S is the part of the paraboloid z = x²+y² that lies inside the cylinder x²+y² = 1, oriented upward.
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