Use Green's Theorem to Evaluate Where C Is the Circle of Radius

question 62

Essay

Use Green's Theorem to evaluate $\int _ { c } \left( \left( \cos x ^ { 2 } + e ^ { x ^ { 2 } } + 3 y \right) \vec { i } + \left( e ^ { 2 \sin y } + 4 x + \cos y ^ { 4 } \right) \vec { k } \right) \cdot \overrightarrow { d r }$ where C is the circle of radius $\sqrt { 3 } ,$ centered at $\left( - 1 , e ^ { 10 } , \ln 13 \right)$ oriented in a counter-clockwise direction.

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