Stokes’ Theorem for line integrals Evaluate the line integral ∮ C F ⋅ d r using Stokes’ Theorem. Assume C has counterclockwise orientation. 57. F = 〈 xz , yz , xy 〉; C is the circle x 2 + y 2 = 4 in the xy -plane.
Stokes’ Theorem for line integrals Evaluate the line integral ∮ C F ⋅ d r using Stokes’ Theorem. Assume C has counterclockwise orientation. 57. F = 〈 xz , yz , xy 〉; C is the circle x 2 + y 2 = 4 in the xy -plane.
Solution Summary: The author analyzes Stokes' Theorem: Let S be an oriented surface with a piecewise-smooth closed boundary C whose orientation is consistent with that of S.
Stokes’ Theorem for line integralsEvaluate the line integral
∮
C
F
⋅
d
r
using Stokes’ Theorem. Assume C has counterclockwise orientation.
57.F = 〈xz, yz, xy〉; C is the circle x2 + y2 = 4 in the xy-plane.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
(b) Evaluate the line integral
Jo dzalong the simple
closed contour C shown in
the diagram.
-2 -1
2j
o
1
2
Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise.
2x + 3y dx + e
-3y
dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1).
Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.
3 In(3 + y) dx -
-dy, where C is the triangle with vertices (0,0), (6, 0), and (0, 12)
ху
3+y
ху
dy =
3 In(3 + y) dx -
3+ y
Chapter 17 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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