In classical mechanics, and mainly when studying the Hamiltonian formalism, the quantity $$ \oint p \ dq $$ is usually referred as an area in the phase space, and can be computed graphically as such. Could someone explain me why this integral represents such an area? Is it simply notation, or does it involve something more?
I know that a general volume in phase space is $$ \int dq_1 \dots dq_n dp_1 \dots dp_n $$ and probably this result is related to that area, but I don't see how. Thanks in advance.