2-6 Use Stokes' Theorem to evaluate ff, curl F. ds. 2. F(x, y, z) = x² sin zi + y2j + xy k, S is the part of the paraboloid z = 1 - x² - y² that lies above the xy-plane, oriented upward 3. F(x, y, z) = ze'i + x cos y j + xz sin y k, S is the hemisphere x² + y² + z² = 16, y = 0, oriented in the direction of the positive y-axis 4. F(x, y, z) = tan¹(x²yz²)i + x²yj + x²z²k, S is the cone x = √y² + 2²,0 ≤ x ≤ 2, oriented in the direction of the positive x-axis 5. F(x, y, z) = xyz i + xy j + x²yz k, S consists of the top and the four sides (but not the bottom) of the cube with vertices (±1, ±1, ±1), oriented outward
2-6 Use Stokes' Theorem to evaluate ff, curl F. ds. 2. F(x, y, z) = x² sin zi + y2j + xy k, S is the part of the paraboloid z = 1 - x² - y² that lies above the xy-plane, oriented upward 3. F(x, y, z) = ze'i + x cos y j + xz sin y k, S is the hemisphere x² + y² + z² = 16, y = 0, oriented in the direction of the positive y-axis 4. F(x, y, z) = tan¹(x²yz²)i + x²yj + x²z²k, S is the cone x = √y² + 2²,0 ≤ x ≤ 2, oriented in the direction of the positive x-axis 5. F(x, y, z) = xyz i + xy j + x²yz k, S consists of the top and the four sides (but not the bottom) of the cube with vertices (±1, ±1, ±1), oriented outward
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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Transcribed Image Text:2-6 Use Stokes' Theorem to evaluate ff, curl F. ds.
2. F(x, y, z) = x² sin zi + y2j + xy k,
S is the part of the paraboloid z = 1 - x² - y² that lies
above the xy-plane, oriented upward
3. F(x, y, z) = ze'i + x cos y j + xz sin y k,
S is the hemisphere x² + y² + z² = 16, y = 0, oriented in
the direction of the positive y-axis
4. F(x, y, z) = tan¹(x²yz²)i + x²yj + x²z²k,
S is the cone x = √y² + 2²,0 ≤ x ≤ 2, oriented in the
direction of the positive x-axis
5. F(x, y, z) = xyz i + xy j + x²yz k,
S consists of the top and the four sides (but not the bottom)
of the cube with vertices (±1, ±1, ±1), oriented outward
ww
YU.
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