the line integral    (1,2,3) (2,0,0) (xdx ydy zdz) is independent of path or not.

Describe the Taylor’s theorem for functions of two variables Jacobeans.

Evaluate ]dxdy )x y(dzdx )y z(dydz )x z([ S ∫∫ + + + + + where S: x2 +y2 +z2 = 1

Find volume of the region bounded by the first octant section cut from the region inside the cylinder x2 +y2 =1 and by the planes y=0, z=0, x=y.

In usual notations prove that, = ∇ ∫∫∫ R f dv 2 ∂ ∫∫ ∂ S dA.

In usual notations prove that, = ∇ ∫∫∫ R f dv 2 ∂ ∫∫ ∂ S dA

Evaluate ∫ ∫ 1 0 2 2 2 0 x y dxdy π .

Check whether the line integral ∫ + + (1,2,3) (2,0,0) (xdx ydy zdz) is independent of path or not. 

Verify Stoke's theorem for v y i x j 3 3  and surface S: the circular disk− = x 2 +y2 1, z=0.≤