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

Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem.

âˆ«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.

âˆ«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,θ) = (x, xcosθ, xsinθ)

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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.