Use Green’s Theorem to evaluate the line integral along the given positively oriented curve.
7. ∫C (y + e ) dx + (2x + cos y2) dy,
C is the boundary of the region enclosed by the parabolas y = x2 and x = y2
To evaluate: The line integral using Green’s Theorem.
Line integral is and curve C is boundary of region enclosed by parabolas and .
Consider a positively oriented curve C which is piece-wise smooth, simple closed curve in plane with domain D. Then,
is a continuous first-order partial derivative of P,
is a continuous first-order partial derivative of Q, and
P and Q have continuous partial derivatives.
The curve C is positively oriented, piecewise-smooth, and simply closed curve with domain and hence Green’s theorem is applicable.
Compare the two expressions and .
Find the value of .
Find the value of .
Re-modify the equation (1)
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