Compute the line integral of \(\mathbf{F}(x, y)=\left\langle x^{3}, 4 xightangle\) along the path from \(A\) to \(B\) in Figure 19. To save work, use Green's Theorem to relate this line integral to the line integral along the vertical path from \(B\) to \(A\).

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THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D is a simple closed curve, oriented counterclockwise. If F and F2 have continuous partial deriva- tives in an open region containing D, then F aF dA f F dx + F dy= - 1 (F-F) da = aD 2