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Answer:
Step-by-step explanation:
a circle will satisfy the conditions of Green's Theorem since it is closed and simple.
Let's identify P and Q from the integral
, and
Now, using Green's theorem on the line integral gives,

Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2