GATE EC 2016 Set 2 — Question 37
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Engineering Mathematics → Vector Calculus → Gauss, Stokes & Green's Theorems
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Question
Suppose is the closed curve defined as the circle with oriented anti-clockwise. The value of over the curve equals ________
Correct answer
-0.03 to 0.03
Solution
By Green's theorem, for a positively (anti-clockwise) oriented closed curve bounding region :Here and , soand the integrand is . Hence the line integral over the unit circle is(Equivalently, is an exact differential, so its integral around any closed curve vanishes.)Answer:
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