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# Integrals, Green's Theorem, Positively Oriented Curve, Ellipse, Vector Equation and Surfaces

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Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem.
∫c xdx + ydy. C consists of the line segments from (0,1) to (0,0)...and the parabola y = 1 -x^2....

Use Green's theorem to evaluate the line intgral along the positively oriented curve.
∫c sin y dx + x cos y dy C is the ellipse x^2 + xy + y^2 = 1

Identify the surface wth the given vector equation.
r(x,&#952;) = (x, xcos&#952;, xsin&#952;)

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Solution.

Method 1. Directly calculation.

So,

Method 2. use ...

#### Solution Summary

Integrals, Green's Theorem, Positively Oriented Curve, Ellipse, Vector Equation and Surfaces are investigated. The solution is detailed and well presented.

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