Evaluate the line integral f (x + y) dr 2xydy on the closed curve C...

 

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Evaluate the line integral f (x² + y²) dr − 2xydy on the closed curve C traversed counterclockwise C = C₁UC₂, where C₁ = {(x, y): -2≤ x ≤ 2 and y = 0} and C₂ = {(x, y) : x² + y² = 4 and y ≥ 0}. Evaluate the line integral f (x² + y²) dr − 2xydy on the closed curve C traversed counterclockwise C = C₁UC₂, where C₁ = {(x, y): -2≤ x ≤ 2 and y = 0} and C₂ = {(x, y) : x² + y² = 4 and y ≥ 0}.