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Analytic Solution to Integral of Polynomial

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This example shows how to use thepolyintfunction to integrate polynomial expressions analytically. Use this function to evaluate indefinite integral expressions of polynomials.

Define the Problem

Consider the real-valued indefinite integral,

∫ ( 4 x 5 - 2 x 3 + x + 4 ) d x

The integrand is a polynomial, and the analytic solution is

2 3 x 6 - 1 2 x 4 + 1 2 x 2 + 4 x + k

where k is the constant of integration. Since the limits of integration are unspecified, theintegralfunction 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 ofx。

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

Integrate the Polynomial Analytically

Integrate the polynomial analytically using thepolyintfunction. Specify the constant of integration with the second input argument.

k = 2; I = polyint(p,k)
I =1×70.6667 0 -0.5000 0 0.5000 4.0000 2.0000

The output is a vector of coefficients for descending powers ofx。这个结果与解析解,but has a constant of integrationk = 2。

See Also

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