This is just a good ole summary section.  Nothing new.  Now you can just get all your main equations from the chapter in one nice easy section!

Fundamental Theorem of Calculus:

∫[a,b] (F'(x)dx) = F(b) - F(a)

Produces a distance between two values, aka a straight line between values at a and b.  Ultimate relates an integral to function values.

Fundamental Theorem for Line Integrals

∫[C] (Ñf ∙ dr) = f(r(b)) - f(r(a))

Produces an arc length between two values, aka a curve C between values at r(a) and r(b).  Ultimately relates a line integral to values of vector-valued functions.

Green's Theorem

∫∫[D] ((∂Q/∂x - ∂P/∂y)dA) = ∫[C] (Pdx + Qdy)

Produces the area of a region D bounded by a curve C, taking counterclockwise as positive orientation.  Ultimately relates a double integral to a line integral.

Stokes's Theorem

∫∫[S] (curl F ∙ dS) = ∫[C] (F ∙ dr)

Considers only a surface (positive oriented with n outward) and a boundary curve on some area of this surface and produces the area of this section.  Ultimately relates a surface integral to a line integral.

Divergence Theorem

∫∫∫[E] (div F dV) = ∫∫[S] (F ∙ dS)

Produces a volume of a surface given by an enclosed region E, positive oriented with n outward.  Ultimately relates a triple integral to a surface integral.