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==4-x² - y² for which z ≥ 0 with upw= rcle x² + y² = 4 that forms the boundar

==4-x² - y² for which z ≥ 0 with upw= rcle x² + y² = 4 that forms the boundar

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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Using stokes theorem

1) Verify Stoke's Theorem for the vector field F(x, y, z) = 2zi + 3x j+5yk, taking S to be the portion of the paraboloid z = 4 - x² - y² for which z≥0 with upward orientation, and C to be the positively oriented circle x² + y² = 4 that forms the boundary of S in the xy - plane. Ans: 127
Transcribed Image Text:1) Verify Stoke's Theorem for the vector field F(x, y, z) = 2zi + 3x j+5yk, taking S to be the portion of the paraboloid z = 4 - x² - y² for which z≥0 with upward orientation, and C to be the positively oriented circle x² + y² = 4 that forms the boundary of S in the xy - plane. Ans: 127
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