Dash Dash The dash is a punctuation mark that is similar in appearance to and , but differs from these symbols in both length and height. The most common versions of the dash are the en dash (–), equal to half the height of the font; the em dash (—), twice as long as the en dash; and the horizontal bar (―), whose length varies across typefaces. Historically, the names of en dash and em dash were loosely related to the width of a lower-case "n" and upper-case "M", respectively, in commonly used typefaces. Usage varies both within English and in
Trapezoidal rule as a change of variables to express arbitrary integrals in terms of periodic integrals, at which point the trapezoidal rule can be applied accurately. Trapezoidal rule In mathematics, and more specifically in numerical analysis, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral. The trapezoidal rule works by approximating the region under the graph of the function formula_2 as a trapezoid and calculating its area. It follows that formula_3, where formula_4 and formula_5. The trapezoidal rule may be viewed as the result obtained by averaging the left and right