Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Two-third rule than freight trains. On such tracks, the two-third rule applies to freight trains. The two-third rule means that the speed limit for a freight train is generally about two-thirds of the speed limit for an EMU. For example, the Dartford Loop Line has a speed limit of 60 mph for EMUs between Lee and Crayford. A freight train on this track is therefore limited to two-thirds of 60 mph, i.e. 40 mph. Two-third rule Two-third rule is British railway safety rule. For safety reasons, speed limits are imposed on trains running on a railway line. Many factors can affect the