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Multivariable calculus

Course: Multivariable calculus > Unit 5

Lesson 2: Green's theorem

Circulation form of Green's theorem

Assume that C is a positively oriented, piecewise smooth, simple, closed curve. Let R be the region enclosed by C.

Use the circulation form of Green's theorem to rewrite \oint, start subscript, C, end subscript, 4, x, natural log, left parenthesis, y, right parenthesis, d, x, minus, 2, d, y as a double integral.

(Choice A)
\iint, start subscript, R, end subscript, start fraction, minus, 4, x, divided by, y, end fraction, d, A
(Choice B)
\iint, start subscript, R, end subscript, 4, x, left parenthesis, y, natural log, left parenthesis, y, right parenthesis, minus, y, right parenthesis, d, A
(Choice C)
\iint, start subscript, R, end subscript, 2, x, minus, 4, x, left parenthesis, y, natural log, left parenthesis, y, right parenthesis, minus, y, right parenthesis, d, A
(Choice D)
\iint, start subscript, R, end subscript, 2, x, minus, start fraction, 4, x, divided by, y, end fraction, d, A
(Choice E)
Green's theorem is not necessarily applicable.

Stuck?

Multivariable calculus

Course: Multivariable calculus > Unit 5

Problem