Use Stokes' Theorem to evaluate (curl (F). ds).F(x,y,z) = 2xî + 2yĵ + z kS is the hemisphere x² + y² + z² = 36is oriented in the direction of the postive y - aixsr(t) 5 cos(t) i + 5 sin(t)j + 6 tky ≥ 00 ≤ t ≤ 2π

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Answered: Use Stokes' Theorem to evaluate ( r(t)…

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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Use Stokes' Theorem to evaluate ( r(t) curl (F) · ds). F(x,y,z) = 2x + 2yj + zk S is the hemisphere x² + y² + z² = 36 y ≥ 0 is oriented in the direction of the postive y - aixs 5 cos (t) + 5 sin(t)j + 6 tk = 0 ≤ t ≤ 2π