be the circle (x − 1)2 + y2 = 1, oriented counter clockwise. Then the value of the line integralisa)6πb)8πc)12πd)14πCorrect answer is option 'B'. Can you explain this answer?

Question

be the circle (x &minus; 1)2 + y2 = 1, oriented counter clockwise. Then the value of the line integralisa)6&pi;b)8&pi;c)12&pi;d)14&pi;Correct answer is option 'B'. Can you explain this answer?

Answer

By Green's Theorem,

Now by using polar x = rcosθ, y = r sinθ. r = 0 to 2 cosθ, θ = 0 to 2θ.
we obtain the solution.

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