Calculus 3 Quiz
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Let F=(y3−z,z3−x,x3−y)\mathbf{F} = (y^3 - z, z^3 - x, x^3 - y) and let CC be the curve of intersection between the cylinder x2+y2=1x^2 + y^2 = 1 and the plane z=x+yz = x + y, oriented counterclockwise when viewed from the point (0,0,10)(0, 0, 10). A student computes ∮CF⋅dr\oint_C \mathbf{F} \cdot d\mathbf{r} using Stokes' theorem with the disk x2+y2≤1x^2 + y^2 \leq 1 in the plane z=x+yz = x + y as the surface. What is the most likely source of error if the student gets 3π3\pi instead of the correct answer −3π-3\pi?
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