Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = yi + xj + z²k, s is the helicoid (with upward orientation) with vector equation r(u, v) = u cos(v)i + u sin(v)j + vk, 0 ≤ u≤ 4,0 ≤ v ≤ 2π

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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"[[F.
F. ds for the given vector field F and the oriented surface S. In other words, find the flux
Evaluate the surface integral
of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = yi + xj + z²k, S is the helicoid (with upward orientation) with vector equation
r(u, v) = u cos(v)i + u sin(v)j + vk, 0 ≤ u ≤ 4,0 ≤ v ≤ 2π
Transcribed Image Text:"[[F. F. ds for the given vector field F and the oriented surface S. In other words, find the flux Evaluate the surface integral of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = yi + xj + z²k, S is the helicoid (with upward orientation) with vector equation r(u, v) = u cos(v)i + u sin(v)j + vk, 0 ≤ u ≤ 4,0 ≤ v ≤ 2π
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