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Multivariable & Vectorhard
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Evaluate the line integral ∮CF⃗⋅dr⃗\oint_C \vec{F} \cdot d\vec{r}∮C​F⋅dr where F⃗=⟨y+esin⁡x,x+cos⁡(y2)⟩\vec{F} = \langle y + e^{\sin x}, x + \cos(y^2) \rangleF=⟨y+esinx,x+cos(y2)⟩ and CCC is the boundary of the region D={(x,y):0≤x≤1,0≤y≤1}D = \{ (x, y) : 0 \le x \le 1, 0 \le y \le 1 \}D={(x,y):0≤x≤1,0≤y≤1} oriented counter-clockwise.