- \(A 5\) We cannot integrate vector fields over \(\mathcal{S}\) because \(\mathcal{S}\) is not orientable, but it is possible to integrate functions over \(\mathcal{S}\). Using a computer algebra system:
(a) Verify that \[
\|\mathbf{N}(u, v)\|^{2}=1+\frac{3}{4} v^{2}+2 v \cos \frac{u}{2}+\frac{1}{2} v^{2} \cos u
\]
(b) Compute the surface area of \(\mathcal{S}\) to four decimal places.

(c) Compute \(\iint_{\mathcal{S}}\left(x^{2}+y^{2}+z^{2}ight) d S\) to four decimal places.