Analytic Solution to Integral of Polynomial
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,
The integrand is a polynomial, and the analytic solution is
where 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 = 1×7 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.