Either directly or by Green's Theorem, evaluate the line integral ∫c e^(-x) (cos y dx - sin y dy), where c is the rectangle with vertices (0, 0), (π, 0), (π, π/2), and (0, π/2).
Added by Kathryn E.
Step 1
The given line integral is \(\int_C e^{-x} (\cos y \, dx - \sin y \, dy)\). This can be expressed in terms of a vector field \(\mathbf{F} = (e^{-x} \cos y, -e^{-x} \sin y)\). Show more…
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