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(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y> conservative? (b) If...

(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y> conservative?

(b) If so, find the associated potential function φ.

(c) Evaluate Integral C F*dr, where C is the straight line path from (0, 0) to (2π, 2π).

(d) Write the expression for the line integral as a single integral without using the fundamental theorem of calculus.

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