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
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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