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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

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

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