Let (mathbf{F}=leftlangle 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}

Question:

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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