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### 27.4 Derivatives and Integrals

Octave comes with functions for computing the derivative and the integral of a polynomial. The functions `polyderiv` and `polyint` both return new polynomials describing the result. As an example we'll compute the definite integral of p(x) = x^2 + 1 from 0 to 3.

         c = [1, 0, 1];
         integral = polyint(c);
         area = polyval(integral, 3) - polyval(integral, 0)
         ⇒ 12

— Function File: polyderiv (c)
— Function File: [q] = polyderiv (b, a)
— Function File: [q, r] = polyderiv (b, a)

> Return the coefficients of the derivative of the polynomial whose coefficients are given by vector c. If a pair of polynomials is given b and a, the derivative of the product is returned in q, or the quotient numerator in q and the quotient denominator in r.

> See also: poly, polyinteg, polyreduce, roots, conv, deconv, residue, filter, polygcd, polyval, polyvalm.

— Function File: polyder (c)
— Function File: [q] = polyder (b, a)
— Function File: [q, r] = polyder (b, a)

> See polyderiv.

— Function File: polyinteg (c)

> Return the coefficients of the integral of the polynomial whose coefficients are represented by the vector c.

> The constant of integration is set to zero.

> See also: polyint, poly, polyderiv, polyreduce, roots, conv, deconv, residue, filter, polyval, polyvalm.

— Function File: polyint (c, k)

> Return the coefficients of the integral of the polynomial whose coefficients are represented by the vector c. The variable k is the constant of integration, which by default is set to zero.

> See also: poly, polyderiv, polyreduce, roots, conv, deconv, residue, filter, polyval, polyvalm.