polyint

Polynomial integration

Syntax

q = polyint(p,k)

q = polyint(p)

Description

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

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

Examples

Integrate Quartic Polynomial

Evaluate the definite integral

$$I={\int }_{-1}^3(3x^4-4x^2+10x-25)dx.$$

Create a vector to represent the polynomial integrand $$3x^4-4x^2+10x-25$$. The ${\mathit{x}}^3$ term is absent and thus has a coefficient of 0.

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

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

q = polyint(p)

q = 1×6

    0.6000         0   -1.3333    5.0000  -25.0000         0

Find the value of the integral 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

$$I={\int }_0^2(x^5-x^3+1)(x^2+1)dx$$

Create vectors to represent the polynomials $$p(x)=x^5-x^3+1$$ and $$v(x)=x^2+1$$.

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 = 1×9

    0.1250         0         0         0   -0.2500    0.3333         0    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

p — Polynomial coefficients

vector

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 $$3.13x^2-2.21x+5.99$$.

For more information, see Create and Evaluate Polynomials.

Data Types: single | double
Complex Number Support: Yes

k — Constant of integration

numeric 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

q — Integrated polynomial coefficients

row vector

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).