Let \(\mathbf{F}=\left\langle y^{2}, x^{2}, z^{2}ightangle\). Show that
\[
\int_{C_{1}} \mathbf{F} \cdot d \mathbf{r}=\int_{C_{2}} \mathbf{F} \cdot d \mathbf{r}
\]
for any two closed curves going around a cylinder whose central axis is the z-axis as shown in Figure 21.

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