4 Let

\\\\Phi :D->R^(3)

be the parametrization of the helicoids

S=\\\\Phi (D)

, where\

\\\\Phi (r,\\\\theta )=(rcos\\\\theta ,rsin\\\\theta ,\\\\theta )

and

D

is the region where

0

.\ Suppose that

S

has a mass density

m(x,y,z)=2\\\\sqrt(x^(2)+y^(2))

at

(x,y,z)inS

.\ Find the total mass of the surface. (12 points)

4 Let :DR3 be the parametrization of the helicoids S=(D), where (r,)=(rcos,rsin,) and D is the region where 02,0r1. Suppose that S has a mass density m(x,y,z)=2x2+y2 at (x,y,z)S. Find the total mass of the surface. (12 points)