Question: Use Stokes' Theorem to evaluate the integral [int_{C}-y^{3} d x+x^{3} d y-z^{3} d z] for (C) the (positively oriented) curve of intersection between the cylinder

Use Stokes' Theorem to evaluate the integral

\[\int_{C}-y^{3} d x+x^{3} d y-z^{3} d z\]

for \(C\) the (positively oriented) curve of intersection between the cylinder \(x^{2}+y^{2}=1\) and the plane \(x+y+z=1\).

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