what is integration

Integration is the process of finding an anti-derivative of a given function f. ‘Integrate f’ means ‘find an anti-derivative of f’. Such an anti-derivative may be called an indefinite integral of f and be denoted by ∫f(x) dx The term ‘integration’ is also used for any method of evaluating a definite integral. The definite integral can be evaluated if an anti-derivative Φ of f can be found, because then its value is Φ(b) − Φ(a). (This is provided that a and b both belong to an interval in which f is continuous.) However, for many functions f, there is no anti-derivative expressible in terms of elementary functions, and other methods for evaluating the definite integral have to be sought, one such being so-called numerical integration.