This example shows how to use the `polyint`

function
to integrate polynomial expressions analytically. Use this function
to evaluate indefinite integral expressions of polynomials.

**Define the Problem**

Consider the real-valued indefinite integral,

$$\int (4{x}^{5}-2{x}^{3}+x+4)dx}.$$

The integrand is a polynomial, and the analytic solution is

$$\frac{2}{3}{x}^{6}-\frac{1}{2}{x}^{4}+\frac{1}{2}{x}^{2}+4x+k,$$

where *k* is the constant of integration. Since
the limits of integration are unspecified, the `integral`

function
family is not well-suited to solving this problem.

**Express the Polynomial with a Vector**

Create a vector whose elements represent the coefficients for
each descending power of *x*.

p = [4 0 -2 0 1 4];

**Integrate the Polynomial Analytically**

Integrate the polynomial analytically using the `polyint`

function.
Specify the constant of integration with the second input argument.

k = 2; I = polyint(p,k)

I = 0.6667 0 -0.5000 0 0.5000 4.0000 2.0000

The output is a vector of coefficients for descending powers
of *x*. This result matches the analytic solution
above, but has a constant of integration `k = 2`

.

Was this topic helpful?