# polyint

Polynomial integration

## Syntax

• q = polyint(p,k)
example
• q = polyint(p)
example

## Description

example

q = polyint(p,k) returns the integral of the polynomial represented by the coefficients in p using a constant of integration k.

example

q = polyint(p) assumes a constant of integration k = 0.

## Examples

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### Integrate Quartic Polynomial

Evaluate

Create a vector to represent the polynomial .

p = [3 0 -4 10 -25]; 

Use polyint to integrate the polynomial using a constant of integration equal to 0.

q = polyint(p) 
q = 0.6000 0 -1.3333 5.0000 -25.0000 0 

Find the value of the integral, I, by evaluating q at the limits of integration.

a = -1; b = 3; I = diff(polyval(q,[a b])) 
I = 49.0667 

### Integrate Product of Two Polynomials

Evaluate

Create vectors to represent the polynomials and .

p = [1 0 -1 0 0 1]; v = [1 0 1]; 

Multiply the polynomials and integrate the resulting expression using a constant of integration k = 3.

k = 3; q = polyint(conv(p,v),k) 
q = Columns 1 through 7 0.1250 0 0 0 -0.2500 0.3333 0 Columns 8 through 9 1.0000 3.0000 

Find the value of I by evaluating q at the limits of integration.

a = 0; b = 2; I = diff(polyval(q,[a b])) 
I = 32.6667 

## Input Arguments

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### p — Polynomial coefficientsvector

Polynomial coefficients, specified as a vector. For example, the vector [1 0 1] represents the polynomial ${x}^{2}+1$, and the vector [3.13 -2.21 5.99] represents the polynomial $3.13{x}^{2}-2.21x+5.99$.

Data Types: single | double
Complex Number Support: Yes

### k — Constant of integrationnumeric scalar

Constant of integration, specified as a numeric scalar.

Example: polyint([1 0 0],3)

Data Types: single | double
Complex Number Support: Yes

## Output Arguments

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### q — Integrated polynomial coefficientsrow vector

Integrated polynomial coefficients, returned as a row vector. For more information, see Create and Evaluate Polynomials.