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
3-Minute Rule 3-Minute Rule "3-Minute Rule" is the 7th track on the album "Paul's Boutique" by American hip hop group the Beastie Boys, released on July 25, 1989. The track was produced and written by the Beastie Boys & the Dust Brothers, and engineered by Mario Caldato & Allen Abrahamson. Despite its title, the song is actually 3 minutes 39 seconds. It begins with the sound of what is apparently a ping-pong ball being hit back and forth. Then Mike D raps from about the 0:12 mark to around the 1:12 mark. MCA follows from about 1:14 to 2:00. Finally, Ad-Rock takes