Massey logo
Home > College of Sciences > Institute of Fundamental Sciences >
Maths First > Online Maths Help > Calculus > Integration > Definition
MathsFirst logo College of Science Brandstrip
  Home  |  Study  |  Research  |  Extramural  |  Campuses  |  Colleges  |  About Massey  |  Library  |  Fees  |  Enrolment




The process of finding a function, given its derivative, is called anti-differentiation (or integration). If F'(x) = f(x), we say F(x) is an anti-derivative of f(x).


F(x) =cos x is an anti-derivative of sin x, and ex is an anti-derivative of ex.

Note that if F(x) is an anti-derivative of f(x) then F(x) + c, where c is a constant (called the constant of integration) is also an anti-derivative of f(x), as the derivative of a constant function is 0. In fact they are the only anti-derivatives of f(x).

Integration and differentiation are reverse processes

We write the indefinite integral off(x) dx = F(x) + c.

if F'(x) = f(x) . We call this the indefinite integral of f(x) .

Thus in order to find the indefinite integral of a function, you need to be familiar with the techniques of differentiation.

Integration Index | Basics >>

   Contact Us | About Massey University | Sitemap | Disclaimer | Last updated: October 9, 2013     © Massey University 2003