Using Stokes's Theorem In Exercises 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16, use Stokes's Theorem to evaluate F. dr. In each case, C is oriented counterclockwise as viewed from above. 7. F(x, y, z) = 2yi + 3zj+rk C: triangle with vertices (2, 0, 0), (0, 2, 0), and (0, 0, 2) Answer + 8. F(x, y, z) = 4zi + x²j+e³k C: triangle with vertices (4, 0, 0), (0, 2, 0), and (0, 0, 8) 9. F(x, y, z) = z²i+2xj+y²k S: z=1-x² - y², z≥0 Answer 10. F(x, y, z) = 4xzi+yj + 4xyk S: z=9x² - y², z>0 11. F(x, y, z) = z²i+yj + zk S: z = √√√4x² - y² Answer 0 12. F(x, y, z) = x²i+z²j – zyzk S: z = √√4x² - y² 13. F (z, 3+ z) =—lnv+gửi+arctan a²j+k

Using Stokes's Theorem In Exercises 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16, use Stokes's Theorem to evaluate F. dr. In each case, C is oriented counterclockwise as viewed from above. 7. F(x, y, z) = 2yi + 3zj+rk C: triangle with vertices (2, 0, 0), (0, 2, 0), and (0, 0, 2) Answer + 8. F(x, y, z) = 4zi + x²j+e³k C: triangle with vertices (4, 0, 0), (0, 2, 0), and (0, 0, 8) 9. F(x, y, z) = z²i+2xj+y²k S: z=1-x² - y², z≥0 Answer 10. F(x, y, z) = 4xzi+yj + 4xyk S: z=9x² - y², z>0 11. F(x, y, z) = z²i+yj + zk S: z = √√√4x² - y² Answer 0 12. F(x, y, z) = x²i+z²j – zyzk S: z = √√4x² - y² 13. F (z, 3+ z) =—lnv+gửi+arctan a²j+k

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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