In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant.
For example, in the quadratic polynomial, The number 3 is a constant term.
Thus, it is common to speak of the quadratic polynomial where
If the constant term is 0, then it will conventionally be omitted when the quadratic is written out.
Any polynomial written in standard form has a unique constant term, which can be considered a coefficient of
This also applies to multivariate polynomials.
For example, the polynomial has a constant term of −4, which can be considered to be the coefficient of
For any polynomial, the constant term can be obtained by substituting in 0 instead of each variable; thus, eliminating each variable.
Therefore the antiderivative is only determined up to an unknown constant term, which is called "the constant of integration" and added in symbolic form (usually denoted as
based on the properties of trigonometric derivatives.
(the antiderivative), plus an arbitrary constant:
, the derivative of the right-hand side of the equation is equal to the left-hand side of the equation.