Newton's Law in Integral form

Each of the Maxwell's equations has both an integral and differential form. Schroedinger's equation is a differential equation and, apparently (I haven't studied it yet), Feynman's path integrals are an equivalent formulation. Newton has got a differential equation $F = \dot p$. Is there an equivalent integral formulation of Newton's law? Would it even be useful if there were?

• Well Newton's formula for gravity is identical to Guass's Law for electrostatics: Poisson's Equation. I only comment because that's not exactly what you are asking about. – Jared Mar 23 '15 at 6:20

$p(t) = \int_0^tf(t')dt'$
• I would suggest that the it should be from $t_0$ to $t$ rather than $0$ to $t$--but I'm not sure it matters. – Jared Mar 23 '15 at 6:17
• Sure, writing the lower limit as $t_0$ generalises the integral form as this can later be set to 0 or whatever, as necessary. – Dai Mar 23 '15 at 6:52
• Or &p(t) = \int_{t_0}^{t} m(t')a(t') dt$to be even more general... – Dai Mar 23 '15 at 6:54 • @CStarAlgebra can you define your variables? Is$t' = t$? Is$f$the resultant force, that is$\sum \vec F= m \vec a\$? – Armadillo May 27 '16 at 13:47