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R is a closed planar region as shown by the shaded area in the figure below. Its boundary C consists of the circles C1 and C2.

If  are all continuous everywhere in R, Green’s theorem states that


Which one of the following alternatives correctly depicts the direction of integration along C?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
R is a closed planar region as shown by the shaded area in the figure ...

The region R is bounded by two closed circles C1 and C2, so it is doubly connected. To apply it in Green’s theorem, we need to convert it into simply connected region. For it, we apply cut AD and consider the region R having simple closed curve ABCADEFDA in the anticlockwise direction. So, the directions shown in figure, (c) is correct option.
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R is a closed planar region as shown by the shaded area in the figure ...

The region R is bounded by two closed circles C1 and C2, so it is doubly connected. To apply it in Green’s theorem, we need to convert it into simply connected region. For it, we apply cut AD and consider the region R having simple closed curve ABCADEFDA in the anticlockwise direction. So, the directions shown in figure, (c) is correct option.
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R is a closed planar region as shown by the shaded area in the figure below. Its boundary C consists of the circles C1 and C2.Ifare all continuouseverywhere in R, Green’s theorem states thatWhich one of the following alternatives correctly depicts the direction of integration along C?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?
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