Integral Calculus Principle

An overview of integration methods

Methods of addressing integration problems

  • Technology - CAS programs, such as Mathematica, Maple and Derive, are capable of calculating extremely complicated integrals, and increasingly modern research facilities are being equipped with such programs.
  • Tables - Prior to the development of CAS programs, scientists relied heavily on tables for calculating the difficult integrals that arise in applications. Such tables have been compiled for many years, incorporating skill and experience of many people.
  • Transformation Methods - These are methods for converting unknown to known integrals. They include replacement u, algebraic manipulation of the integrated, among other methods.

None of the three methods is perfect; for example, CAS programs often find integrals that they are unable to integrate and produce answers that are sometimes overly complicated, tables are not exhaustive and may not include an integral of interest, and transformation methods depend on human ingenuity, which may not be suitable for difficult problems.

Next: Integration Formulas