b) Given

vec(F)(x,y,z)=(xy^(2)-tanx)vec(i)+(x^(2)y+\\\\pi ^(2))vec(j)+(e^(z)-3xy^(2))vec(k)

. Use Stokes' Theorem to evaluate

o\\\\int_C vec(F)(*)/(b)ar (dr)

where

C

is the boundary of the rectangle of a plane

2z=6-3y

that lies above the region

R={(x,y,z):0=0}

and

C

is oriented counterclockwise as shown in Figure 4.\ (12 marks)

b) Given F(x,y,z)=(xy2tanx)i+(x2y+2)j+(ez3xy2)k. Use Stokes' Theorem to evaluate CFdr where C is the boundary of the rectangle of a plane 2z=63y that lies above the region R={(x,y,z):0x1,0y2,z0} and C is oriented counterclockwise as shown in Figure 4. (12 marks)