Evaluate the definite integral

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

Evaluate

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