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Evaluate the following "curly" surface integrals (V x F). ds. (a) F(x, y, z) = yi – xj + zx³y²k and S = {(x, y, z) : x² + y² + 3z² = 1 and z ≤ 0}. (b) F(x, y, z) = (x² + y − 4,3xy, 2xz + z²) and S = {(x, y, z) = x² + y² + z² = 16 and z ≥ 0}.

Evaluate the following "curly" surface integrals (V x F). ds. (a) F(x, y, z) = yi – xj + zx³y²k and S = {(x, y, z) : x² + y² + 3z² = 1 and z ≤ 0}. (b) F(x, y, z) = (x² + y − 4,3xy, 2xz + z²) and S = {(x, y, z) = x² + y² + z² = 16 and z ≥ 0}.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.5: The Area Between Two Curves
Problem 21E
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Evaluate the following "curly" surface integrals (V x F). ds. (a) F(x, y, z) = yi – xj + zx³y²k and S = {(x, y, z) : x² + y² + 3z² = 1 and z ≤ 0}. (b) F(x, y, z) = (x² + y − 4,3xy, 2xz + z²) and S = {(x, y, z) = x² + y² + z² = 16 and z ≥ 0}.
Transcribed Image Text:Evaluate the following "curly" surface integrals (V x F). ds. (a) F(x, y, z) = yi – xj + zx³y²k and S = {(x, y, z) : x² + y² + 3z² = 1 and z ≤ 0}. (b) F(x, y, z) = (x² + y − 4,3xy, 2xz + z²) and S = {(x, y, z) = x² + y² + z² = 16 and z ≥ 0}.
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