Use Green’s Theorem to evaluate ∫C F · dr. (Check the orientation of the curve before applying the theorem.)
13. F(x, y) = ⟨y − cos y, x sin y⟩, C is the circle (x − 3)2 + (y + 4)2 = 4 oriented clockwise
To evaluate: The line integral using Green’s Theorem.
Vector field is and curve C is a circle oriented clockwise.
Consider a positively oriented curve C which is piece-wise smooth, simple closed curve in plane with domain D. Then the line integration of vector field over curve C is,
is continuous first-order partial derivative of P,
is continuous first-order partial derivative of Q, and
P and Q have continuous partial derivatives.
Write the equation of a circle.
is center, and
r is radius.
Compare the equations and .
The curve C is a disk with center and radius 2. Curve C is piecewise-smooth, and simply closed curve with domain D and curve C is in transverse clockwise direction and hence possess the positive orientation. Therefore, the Green’s theorem is applicable.
Compare the two vector fields and .
Find the value of .
Find the value of
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: An Applied Approach (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendental Functions
Finite Mathematics and Applied Calculus (MindTap Course List)
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Understanding Basic Statistics
Probability and Statistics for Engineering and the Sciences
Mathematical Applications for the Management, Life, and Social Sciences
Elementary Technical Mathematics
Elementary Geometry For College Students, 7e
Contemporary Mathematics for Business & Consumers
Mathematical Excursions (MindTap Course List)
Calculus of a Single Variable
Calculus: Early Transcendental Functions (MindTap Course List)
Single Variable Calculus: Early Transcendentals
Elements Of Modern Algebra
Trigonometry (MindTap Course List)
Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students