设空间曲线 $L:\left\{\begin{array}{l}z=x^2+2 y^2, \\ z=6-2 x^2-y^2,\end{array}\right.$ 从 $z$ 轴正向往负向看为逆时针方向, 计算曲线积分
$$
I=\oint_L\left(z^2-y\right) \mathrm{d} x+\left(x^2-z\right) \mathrm{d} y+\left(x-y^2\right) \mathrm{d} z
$$
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