Evaluate Where C Is the Positively-Oriented Boundary of the Half Disk

question 173

Short Answer

Evaluate $\oint _ { C } \left( x \cos x + e ^ { \sin x } + 3 y \right) d x + \left[ 5 x + \left( 1 + y ^ { 2 } \right) ^ { 3 } + \cos \left( e ^ { y } + y ^ { 2 } \right) \right] d y$ where C is the positively-oriented boundary of the half disk D: $x ^ { 2 } + y ^ { 2 } \leq 2 , y \geq 0$ .

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