Question 8: Assume the drive flies in the gravitational field
\textbf{F}(x, y, z) = [x^7 + xy^2z^2, x^2yz^2, x^2y^2z]
along the path $C: \textbf{r}(t) = [t \cos t, t \sin t, t(5\pi - t)]$ with $0 \le t \le 5\pi$.
(a) Compute the work $\int_0^{5\pi} \textbf{F} \cdot d\textbf{r}$.
(b) Compute $d = \left| \int_0^{5\pi} \textbf{r}'(t)dt \right|.$