Problem. 9: Use the Divergence Theorem to calculate the surface integralF. dS, whereF(x, y, z) = xz² i+3+ cos(2) ) j+ (² z + y?) kand S is the top half of the sphere x2 + y² + z² = 9.Note that S is not a closed surface. First, compute the integrals over S1 and S2, where Sı is the disk x? + y? < 9, oriented downward, and S2 = S1 USis a closed surface.F. dS? dy dxS1a?+y?<9

Given the field equation, Fx,y,z=xz2i+y33+coszj+ x2z+y2k The surface S is the top half of the sphere…

Problem. 9: Use the Divergence Theorem to calculate the surface integral || F. dS, where S F(x, y, z) = xz² i + 3 + cos(2) ) j+ (æ²z+ y²) k and S is the top half of the sphere x² + y? + z? = 9. Note that S is not a closed surface. First, compute the integrals over Si and S2, where Si is the disk a? + y² < 9, oriented downward, and S2 = S1 U S is a closed surface. F. dS = ? dy dx z²+y²<9 ?

Problem. 9: Use the Divergence Theorem to calculate the surface integral || F. dS, where S F(x, y, z) = xz² i + 3 + cos(2) ) j+ (æ²z+ y²) k and S is the top half of the sphere x² + y? + z? = 9. Note that S is not a closed surface. First, compute the integrals over Si and S2, where Si is the disk a? + y² < 9, oriented downward, and S2 = S1 U S is a closed surface. F. dS = ? dy dx z²+y²<9 ?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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