Explanation Theorem used: “Green’s Theorem: Let C be a piecewise smooth, simple closed curve with positive orientation about a region D . Suppose F ( x , y ) = P ( x , y ) i + Q ( x , y ) j , where P ( x , y ) and Q ( x , y ) have continuous partials in an open region containing D. Then ∮ C F ⋅ d r = ∬ D ( ∂ Q ∂ x − ∂ P ∂ y ) d A .” Calculation: Given that, from the figure in question 1, the area of a region enclosed by a closed curve C. Note that evaluating ∬ D 1 d A is one of the way of finding the area of the region D . Rewrite the integrand 1 of the integral ∬ D 1 d A as, ∂ Q ∂ x − ∂ P ∂ y

Study Guide for Stewart's Multivariable Calculus, 8th

8th Edition

ISBN: 9781305271845

Author: Stewart, James

Publisher: Brooks Cole

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Chapter 16.4, Problem 4PT

To determine

To choose: The appropriate option “The area of a region D enclosed by a curve C such as that pictured in question 1, may be evaluated using the line integral”.

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Chapter 16 Solutions

Study Guide for Stewart's Multivariable Calculus, 8th

Ch. 16.1 - For F(x,y)=(x+y)i+(2x4y)j, which vector, a, b, c,...Ch. 16.1 - Prob. 2PT Ch. 16.1 - Prob. 3PT Ch. 16.1 - True or False: F(x,y)=2yi+2xj is conservative.Ch. 16.2 - A definite integral for C(x+y)ds, where C is the...Ch. 16.2 - True or False: The curve at the right appears to...Ch. 16.2 - A definite integral for CFdr, where F(x,y)=x2i+y2j...Ch. 16.2 - Prob. 4PT Ch. 16.2 - Prob. 5PT Ch. 16.3 - Prob. 1PT

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Double and Triple Integrals; Author: Professor Dave Explains;https://www.youtube.com/watch?v=UubU3U2C8WM;License: Standard YouTube License, CC-BY

To choose: The appropriate option “The area of a region D enclosed by a curve C such as that pictured in question 1, may be evaluated using the line integral”.

Solution Summary: The author explains that evaluating undersetDiint1dA is one way of finding the area of the region D.

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To choose: The appropriate option “The area of a region D enclosed by a curve C such as that pictured in question 1, may be evaluated using the line integral”.

Chapter 16 Solutions