Chapter 18.2, Problem 17E

(a)

To determine

To sketch:

The orientation of the $\partial S$, that is top and bottom circles.

The diagram:

Applying the right hand rule , since we already have the normal in the outward direction so the compatible orientation of the top and bottom parts of the boundary of the surface eventually come out to be opposite. The top one has a counter clockwise orientation while the bottom ha clockwise orientation when viewed from above.

The diagram showing the orientation is:

(b)

To determine

To verify:

Stokes’ Theorem for S and F= <yz²,0,0>

${\displaystyle \underset{C}{\oint }\overrightarrow{F}}·d\overrightarrow{R}$= −9