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42. Use Gauss's Theorem to evaluate fF-ds for F=2x1+xzj + zk where S is a closed surface of the region that is bounded by a sphere x² + y² +2²=4. Answer: 32

42. Use Gauss's Theorem to evaluate fF-ds for F=2x1+xzj + zk where S is a closed surface of the region that is bounded by a sphere x² + y² +2²=4. Answer: 32

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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42. Use Gauss's Theorem to evaluate fF.ds for F= 2xi +xzj + zk where S is a closed surface of the region that is bounded by a sphere x² + y² + z² = 4. Answer: 32 43. Use Gauss's Theorem to evaluate fF-d$ for F=3xyi + xyj + 2zk where S is a closed surface of the region that is bounded by a paraboloid z=3-x² - y² and plane z = 0. Answer: 9x 44. Use Gauss's Theorem to evaluate fF-d$ if F=x³i+y³i+z³k where S is the closed surface of the hemisphere that is bounded by zs√1-x²-y² and zz0. Answer:
Transcribed Image Text:42. Use Gauss's Theorem to evaluate fF.ds for F= 2xi +xzj + zk where S is a closed surface of the region that is bounded by a sphere x² + y² + z² = 4. Answer: 32 43. Use Gauss's Theorem to evaluate fF-d$ for F=3xyi + xyj + 2zk where S is a closed surface of the region that is bounded by a paraboloid z=3-x² - y² and plane z = 0. Answer: 9x 44. Use Gauss's Theorem to evaluate fF-d$ if F=x³i+y³i+z³k where S is the closed surface of the hemisphere that is bounded by zs√1-x²-y² and zz0. Answer:
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