Explanation Given : F = i and S is the oriented half-cylinder S is parameterized by: ϕ ( θ , z ) = ( cos θ , sin θ , z ) , 0 ≤ z ≤ 3 , − π 2 ≤ θ ≤ π 2 cos ≥ 00 ≤ θ ≤ π 2 Hence, T θ = ∂ ϕ ∂ θ = 〈 − sin θ , cos θ , 0 〉 T z = ∂ ϕ ∂ z = 〈 0 , 0 , 1 〉 n = T θ × T z = ( i j k − sin θ cos θ 0 0 0 1

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.5, Problem 18E

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(a) To determine: Whether $\iint_{s} F \cdot d s$ is positive, negative, or zero.

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Chapter 17.5, Problem 17E

Chapter 17.5, Problem 19E

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Chapter 17 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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(a) To determine : Whether ∬ s F ⋅ d s is positive, negative, or zero.

Solution Summary: The author explains that the normal to S is pointing in the outward direction; hence the x -coordinate of n is positive.

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(a) To determine: Whether $\iint_{s} F \cdot d s$ is positive, negative, or zero.

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Chapter 17 Solutions

(a) To determine : Whether ∬ s F ⋅ d s is positive, negative, or zero.

Solution Summary: The author explains that the normal to S is pointing in the outward direction; hence the x -coordinate of n is positive.

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(a) To determine: Whether ∬sF⋅ds is positive, negative, or zero.

Want to see the full answer?

Chapter 17 Solutions

(a) To determine: Whether $\iint_{s} F \cdot d s$ is positive, negative, or zero.