Green's theorem (tangential and normal forms)

Green's Theorem's tangential (circulation) form is \oint_C\mathbf{F}\cdot d\mathbf{r} = \iint_R \operatorname{curl}\mathbf{F}\,dA; its normal (flux) form is \oint_C \mathbf{F}\cdot\mathbf{n}\,ds = \iint_R \operatorname{div}\mathbf{F}\,dA. The two forms aren't separate theorems — the normal form falls out of the tangential form by rotating \mathbf{F} by 90°, since a rotated field's curl is the original field's divergence up to sign. A circulation question uses the tangential form and integrates Q_x-P_y; a flux question uses the normal form and integrates P_x+Q_y.