3. Show that the line integral is independent of path and evaluate the integral.\\
$\int_C (x^2 + 2xy)dx + x^2dy + 2xzdz$,\\
where C runs from (2,1,3) to (4,-1,0).\\
4. Using the Green's Theorem evaluate the line integral\\
$\int_C (y^2 + x)dx + (3x + 2xy)dy$,\\
where C is the circle $x^2 + y^2 = 4$ oriented clockwise.\\
5. Consider the vector field $F(x, y, z) = (x^3 - y, 3x - y, 2 - z^3)$ and compute the\\
divergence of F, $\nabla \cdot F$, and the curl of F, $\nabla \times F$.\\
6. Let Q be the solid bounded by the paraboloid $z = x^2 + y^2$ and the plane $z = 4$,\\
use the Divergence Theorem find the flux of the vector field\\
over the surface $\partial Q$.\
$F(x, y, z) = (x^3, y^3 - x, xy^2)$\\7. Use the Stokes Theorem to evaluate the surface integral $\iint_S (\nabla \times F) \cdot n dS$, where\\
S is the portion of the paraboloid $y = 4 - x^2 - z^2$ with $y > 0$, and F is the vector\\
field\\
$F(x, y, z) = (yx^2, x^2 \cos y, 8x)$.
