Chapter 17.4, Problem 5E

To determine

The following

a) $T_x,T_y\text{ and }n(x,y)$

b) Verify and evaluate using polar coordinates:

${\displaystyle {\iint }_{S}1dS}={\displaystyle {\iint }_D\sqrt{1+x^2+y^2}}dxdy$

c) Verify the following formula and evaluate:

${\displaystyle {\iint }_{S}zdS}={\displaystyle \underset{0}{\overset{\pi /2}{\int }}{\displaystyle \underset{0}{\overset{1}{\int }}(\sin \theta \cos \theta )r^3}}\sqrt{1+r^2}drd\theta$