4 Differentiation and Integration

Recall from §2.8.1 that an integral expression is entered in the syntactic form ∫ integrand ⅆ integrator and is displayed the same way. The derivative operator is entered in a similar form ⅆ derivand ⅆ derivator, but is displayed as ⅆderivandⅆderivator. (See §1.6.1.1 for symbols ∫ and ⅆ.) The integrator and the derivator are often simple variables but can be expressions, in which case they should be parenthesized. An integrator can also be a function definition, in which case the function definition is displayed as a decoration on the integral (see §4.4.2).

Definite integrals use a syntax similar to that of indefinite integrals, with the addition of upper and lower bounds. The form is ∫ lower-bound, upper-bound, integrand ⅆ integrator.

When a definite integral is integrated, the bounds must be carried forward. The syntax is almost the same as in that of definite integrals with “|” in place of “∫”. The full syntactic form is | lower-bound, upper-bound, integrand ⅆ integrator. The form is called a definite integration.