Fundamental Theorem of Calculus¶
$$ \int_a^b F'(x) dx = F(b) - F(a) $$
Fundamental Theorem of Line Integrals¶
$$ \int_{C} {{\nabla}} f \cdot d {\textbf{r}} = f ({\textbf{r}}({\textbf{b}}) - f ({\textbf{r}}({\textbf{a}}))$$
Green's Theorem¶
$$ \int_{D} \left( \frac{\partial Q}{\partial x} -\frac{\partial P}{\partial y} \right) dA = \int_{C} P dx + Q dy $$
Stokes' Theorem¶
$$ \int_{S} \nabla \times {\textbf{F}} \cdot d{\textbf{S}} = \int_{C} {\textbf{F}} \cdot d{\textbf{r}} $$
Divergence Theorem¶
$$\int_V \nabla \cdot {\textbf{F}} dV = \int_S {\textbf{F}} \cdot d{\textbf{S}}$$