Question

Consider the vector force field given by F⃗ = 〈2x + y, 3y + x〉 (a)...

Consider the vector force field given by F⃗ = 〈2x + y, 3y + x〉

(a) Let C1 be the straight line segment from (2, 0) to (−2, 0).

Directly compute ∫ C1 F⃗ · d⃗r (Do not use Green’s Theorem or the Fundamental Theorem of Line Integration)

(b) Is the vector field F⃗ conservative? If it is not conservative, explain why. If it is conservative, find its potential function f(x, y)

Let C2 be the arc of the half-circle of radius 2 from (2, 0) to (−2, 0) with y ≥ 0. Compute ∫ C2 F⃗ · d⃗r

Explain your work and how your answer relates to the answer to part (a).

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