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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
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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Please show the work for question 11 and 13. Explanations are not needed, just the work shown will be sufficient. Thank you!

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 + : 00 00 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 (æ, y, z) =—lnvg+gởi+arctan-j+k Answer S: z = 9-2x - 3y over r = 2 sin 20 in the first octant
Transcribed Image Text: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 + : 00 00 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 (æ, y, z) =—lnvg+gởi+arctan-j+k Answer S: z = 9-2x - 3y over r = 2 sin 20 in the first octant
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