Question - Integration of Polynomials
Solution:
To solve the integral$$\int (8x^3 - x^2 + 5x - 1) dx$$we will integrate each term separately. Recall that the integral of $$x^n$$ with respect to $$x$$ is $$\frac{x^{n+1}}{n+1}$$ plus a constant of integration, for any real number $$n$$ not equal to -1.Here are the steps:$$\int 8x^3 dx = \frac{8}{4}x^{3+1} = 2x^4$$$$\int (-x^2) dx = -\frac{1}{3}x^{2+1} = -\frac{1}{3}x^3$$$$\int 5x dx = \frac{5}{2}x^{1+1} = \frac{5}{2}x^2$$$$\int (-1) dx = -x$$Now combine all terms to get the antiderivative:$$\int (8x^3 - x^2 + 5x - 1) dx = 2x^4 - \frac{1}{3}x^3 + \frac{5}{2}x^2 - x + C$$where $$C$$ is the constant of integration.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com