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14. Which of the following integrals equals the flux of the vector field F(x, y, z) = yj - zk across the surface S consisting of the part of the paraboloid z = x² + y² that lies below the plane z = 1, and has positive orientation? Hint: The k-component of the normal vector must be negative on S. a) + f2r²(1-2sin²0) drde b) +²¹³(1+2sin²0)drd0 -2π c) r²(1-2sin²0) drdo d) - ²r³ (1+2sin²0)drdo e) None of the above -2π

14. Which of the following integrals equals the flux of the vector field F(x, y, z) = yj - zk across the surface S consisting of the part of the paraboloid z = x² + y² that lies below the plane z = 1, and has positive orientation? Hint: The k-component of the normal vector must be negative on S. a) + f2r²(1-2sin²0) drde b) +²¹³(1+2sin²0)drd0 -2π c) r²(1-2sin²0) drdo d) - ²r³ (1+2sin²0)drdo e) None of the above -2π

Advanced Engineering Mathematics
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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14. Which of the following integrals equals the flux of the vector field F(x, y, z) = yj - zk across the surface S consisting of the part of the paraboloid z = x² + y² that lies below the plane z = 1, and has positive orientation? Hint: The k-component of the normal vector must be negative on S. a) + f²r²(1-2sin²0) drdo b) +²¹³(1+2sin²0) drdo c) - ²r²(1-2sin²0) drdo 21 d) - ²r³ (1+2sin²0) drdo e) None of the above
Transcribed Image Text:14. Which of the following integrals equals the flux of the vector field F(x, y, z) = yj - zk across the surface S consisting of the part of the paraboloid z = x² + y² that lies below the plane z = 1, and has positive orientation? Hint: The k-component of the normal vector must be negative on S. a) + f²r²(1-2sin²0) drdo b) +²¹³(1+2sin²0) drdo c) - ²r²(1-2sin²0) drdo 21 d) - ²r³ (1+2sin²0) drdo e) None of the above
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