`polyint`

Integral of a polynomial.

Syntax

q = polyint(p)

Returns the coefficients of the antiderivative of p with constant term 0.

q = polyint(p, k)

Uses k as the constant of integration.

Description

Each coefficient p(i) of x^m is divided by m+1 and the degree goes up by one. For a definite integral between a and b, evaluate the antiderivative at both ends: diff(polyval(polyint(p), [a b])).

The operation is the inverse of polyder, apart from the constant.

Input arguments

p: Coefficient vector, highest power first.
k: Scalar constant of integration (default 0).

Output arguments

q: Coefficients of the antiderivative, one element longer than p.

Example

Antiderivative and definite integral

q = polyint([3 2 1])
polyint([3 2 1], 5)
diff(polyval(q, [0 2]))

Output

q = 1×4

     1     1     1     0
ans = 1×4

     1     1     1     5
ans = 14

polyint