Explore BrainMass

Explore BrainMass

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

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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,θ) = (x, xcosθ, xsinθ)

    Please see the attached file for the fully formatted problems.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:23 pm ad1c9bdddf
    https://brainmass.com/math/integrals/green-s-theorem-positively-oriented-curve-ellipse-42866

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    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.

    $2.49

    ADVERTISEMENT