For other simple methods of numerical integration, look at the Trapezoidal Rule and Simpson's Rule, two staples of high school (or college) calculus.
Since we're talking about gaming, it bears noting that Box2D (and most physics engines, for that matter) uses the Semi-implicit Euler method (http://en.wikipedia.org/wiki/Symplectic_Euler_method). The author of Box2D mentions that this is a better method than Verlet integration because calculating friction requires knowing velocity.
Since we're talking about gaming, it bears noting that Box2D (and most physics engines, for that matter) uses the Semi-implicit Euler method (http://en.wikipedia.org/wiki/Symplectic_Euler_method). The author of Box2D mentions that this is a better method than Verlet integration because calculating friction requires knowing velocity.