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Use Stokes's Theorem to evaluate F. dr. Use a computer algebra system to verify your results. In each case, C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + (2-6y)j + (x² + y²)k, x² + y² ≤ 49 S: the first-octant portion of x2 + z² = 49 over x² + y² = 49 art 1 of 6 The surface S is described by x² + z² = 49 over x² + y² = 49. To evaluate a line integral of F over this surface, write S as z = g(x, y), where g(x, y) = √√√49x². Since S is orientable, it can be described by the function G(x, y, z), where G(x, y, z) = z g(x, y) = z √ x². Therefore, VG(x, y, z)=G(x, y, z)i + · G(x, y, z)j +G(X, Y, y, z)k ду 49 x² i + k.

Use Stokes's Theorem to evaluate F. dr. Use a computer algebra system to verify your results. In each case, C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + (2-6y)j + (x² + y²)k, x² + y² ≤ 49 S: the first-octant portion of x2 + z² = 49 over x² + y² = 49 art 1 of 6 The surface S is described by x² + z² = 49 over x² + y² = 49. To evaluate a line integral of F over this surface, write S as z = g(x, y), where g(x, y) = √√√49x². Since S is orientable, it can be described by the function G(x, y, z), where G(x, y, z) = z g(x, y) = z √ x². Therefore, VG(x, y, z)=G(x, y, z)i + · G(x, y, z)j +G(X, Y, y, z)k ду 49 x² i + k.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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15.8-9

Use Stokes's Theorem to evaluate F(x, y, z) = yzi + (2 − 6y)j + (x² + y²)k, x² + y² ≤ 49 S: the first-octant portion of x² + z² = 49 over x² + y² = 49 Jo F. dr. Use a computer algebra system to verify your results. In each case, C is oriented counterclockwise as viewed from above. Part 1 of 6 The surface S is described by x² + z² = 49 over x² + y² = 49. To evaluate a line integral of F over this surface, write S as z = g(x, y), where g(x, y) = √√49x². Since S is orientable, it can be described by the function G(x, y, z), where G(x, y, z) = z g(x, y) = z v Therefore, VG(x, y, z) = = _G(x, y, z)i + _O_G(x, y, z)j + ₂G(x, y, z)k ax ay √49 - x² i + k.
Transcribed Image Text:Use Stokes's Theorem to evaluate F(x, y, z) = yzi + (2 − 6y)j + (x² + y²)k, x² + y² ≤ 49 S: the first-octant portion of x² + z² = 49 over x² + y² = 49 Jo F. dr. Use a computer algebra system to verify your results. In each case, C is oriented counterclockwise as viewed from above. Part 1 of 6 The surface S is described by x² + z² = 49 over x² + y² = 49. To evaluate a line integral of F over this surface, write S as z = g(x, y), where g(x, y) = √√49x². Since S is orientable, it can be described by the function G(x, y, z), where G(x, y, z) = z g(x, y) = z v Therefore, VG(x, y, z) = = _G(x, y, z)i + _O_G(x, y, z)j + ₂G(x, y, z)k ax ay √49 - x² i + k.
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Use Stokes's Theorem to evaluate F(x, y, z) = yzi + (2 − 6y)j + (x² + y²)k, x² + y² ≤ 49 S: the first-octant portion of x² + z² = 49 over x² + y² = 49 Part 1 of 6 The surface S is described by x² + z² = 49 over x² + y² = 49. To evaluate a line integral of F over this surface, write S as z = g(x, y), where g(x, y) = √√49x². Since S is orientable, it can be described by the function G(x, y, z), where G(x, y, z) = z g(x, y) = z-V 49 Therefore, VG(x, y, z) = curl F = ScF F. dr. Use a computer algebra system to verify your results. In each case, C is oriented counterclockwise as viewed from above. = ə X = i(|| G(x, y, z)i +G(x, y, z)j + G(x, y, z)k дz ?х Part 2 of 6 It is given that F(x, y, z) = yzi + (2 − 6y)j + (x² + y²)k. Therefore, i j k ə Ə əx ду əz yz 2-6y x² + y² 49 49 -². X + k. −(x² + y²) - 0₂ (2 − 6y)) - ³(2x (x² + y²) − 0₂y²) + k( 0 (2 − 6y) - 8yz) y²) əy дz i + (y- - 0) - j(2x - y) + k(0 - z) )j - zk.
Transcribed Image Text:Use Stokes's Theorem to evaluate F(x, y, z) = yzi + (2 − 6y)j + (x² + y²)k, x² + y² ≤ 49 S: the first-octant portion of x² + z² = 49 over x² + y² = 49 Part 1 of 6 The surface S is described by x² + z² = 49 over x² + y² = 49. To evaluate a line integral of F over this surface, write S as z = g(x, y), where g(x, y) = √√49x². Since S is orientable, it can be described by the function G(x, y, z), where G(x, y, z) = z g(x, y) = z-V 49 Therefore, VG(x, y, z) = curl F = ScF F. dr. Use a computer algebra system to verify your results. In each case, C is oriented counterclockwise as viewed from above. = ə X = i(|| G(x, y, z)i +G(x, y, z)j + G(x, y, z)k дz ?х Part 2 of 6 It is given that F(x, y, z) = yzi + (2 − 6y)j + (x² + y²)k. Therefore, i j k ə Ə əx ду əz yz 2-6y x² + y² 49 49 -². X + k. −(x² + y²) - 0₂ (2 − 6y)) - ³(2x (x² + y²) − 0₂y²) + k( 0 (2 − 6y) - 8yz) y²) əy дz i + (y- - 0) - j(2x - y) + k(0 - z) )j - zk.
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