In
calculus, the process of finding a
function whose
derivative is a given function. The term, sometimes used interchangeably with "antidifferentiation," is indicated symbolically with the integral sign
ò. (The
differential dx usually follows to indicate
x as the
variable.) The basic rules of integration are: (1)
ò(
f +
g)
dx =
òfdx +
ògdx (where
f and
g are functions of the variable
x), (2)
òkfdx =
kòfdx (
k is a constant), and (3)
(
C is a constant). Note that any constant value may be added onto an indefinite integral without changing its derivative. Thus, the indefinite integral of 2
x is
x2 +
C, where
C can be any real number. A definite integral is an indefinite integral evaluated over an interval. The result is not affected by the choice for the value of
C.
See also differentiation.
For more information on integration, visit Britannica.com.
