Question - Integral of Polynomial Function
mathindefinite integralintegral of polynomial functionpower rule for integrationterm-by-term integration
Solution:
The integral in the image is an indefinite integral of a polynomial function. To solve the integral, you would integrate each term separately, applying the power rule for integration. Here's the integration term-by-term:∫(8x^3 - x^2 + 5x - 1) dx= ∫8x^3 dx - ∫x^2 dx + ∫5x dx - ∫1 dxNow applying the power rule for integration (which states that ∫x^n dx = x^(n+1)/(n+1) for all n ≠ -1), we get:= 8 * x^(3+1)/(3+1) - x^(2+1)/(2+1) + 5 * x^(1+1)/(1+1) - x + C= 8 * x^4/4 - x^3/3 + 5 * x^2/2 - x + CSimplifying, we have:= 2x^4 - (1/3)x^3 + (5/2)x^2 - x + CSo the integral is:2x^4 - (1/3)x^3 + (5/2)x^2 - x + Cwhere C represents the constant of integration.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com