This example shows how to use the polyint function to integrate polynomial expressions analytically. Use this function to evaluate indefinite integral expressions of polynomials.
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Define the Problem
Consider the real-valued indefinite integral,
The integrand is a polynomial, and the analytic solution is
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.