6. Use the Stokes theorem to calculate the line integral ?c F · r'ds Where F is given by F = [e^y, 0, e^x] around the triangle with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0).
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The curl of F is given by ∇ x F, where ∇ is the del operator. In this case, F=[e0,c], so we have: ∇ x F = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y) Since F=[e0,c], we have Fx = e, Fy = 0, and Fz = c. Therefore, the curl of F is: ∇ x F = (∂c/∂y - Show more…
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