Math Definite integral Definite integral

Definite integral

The result obtained by partition of an interval is always a explicit, fixed number and is called a definite integral.

For a definite integral, use the notation:

$\int_a^b f(x)\,\mathrm{d}x$
(read: the integral of f(x) with respect to x from a to b)
  • $a$ and $b$ are limits of integration
  • $[a; b]$ is the interval of integration
  • $f(x)$ is the integrand
  • $x$ is the variable of integration
  • $dx$ is the differential


The definite integral is a fixed number that depends solely on the function and the limits of integration.

In contrast to indefinite integrals, it can be calculated using partition of an interval or, more simply, with the fundamental theorem of calculus.


For the definite integral, the partitions above the x-axis are positive and those below negative.

More about this under area calculation with integrals.