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Math Help - Green's Theorem

  1. #1
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    Green's Theorem

    Use Green's Theorem to evaluate the line integral along the given positively oriented curve:

    \int_{C}F \cdot dr, F = (y^2 - x^{2}y)i + xy^2j

    C consists of the circle x^2 + y^2 = 16 from (4, 0) to (2\sqrt{2}, 2\sqrt{2}) and the line segments from (2\sqrt{2}, 2\sqrt{2}) to (0, 0) and from (0, 0) to (4, 0).
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  2. #2
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    Quote Originally Posted by wik_chick88 View Post
    Use Green's Theorem to evaluate the line integral along the given positively oriented curve:

    \int_{C}F \cdot dr, F = (y^2 - x^{2}y)i + xy^2j

    C consists of the circle x^2 + y^2 = 16 from (4, 0) to (2\sqrt{2}, 2\sqrt{2}) and the line segments from (2\sqrt{2}, 2\sqrt{2}) to (0, 0) and from (0, 0) to (4, 0).
    \int_{C}F \cdot dr =\int\int_{D}( \frac {\partial {(xy^2)}}{\partial x}-\frac {\partial {(y^2-x^{2}y)}}{\partial y}) dxdy, where D is the region enclosed by the curve, C. Then calculate the double integral in polar coordinates.
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