Question - Solving Polynomial Integral with Power Rule
mathconstant of integrationpower rule integrationsolving polynomial integralintegration of polynomials
Solution:
The integral in the image is:∫(8x^3 - x^2 + 5x - 1)dxTo solve this integral, you need to integrate each term separately with respect to x. The integration of a polynomial involves applying the power rule for integration, which says that for any term ax^n, the integral is (a/(n+1))x^(n+1), assuming n ≠ -1.Here's how you integrate each term:For 8x^3: ∫8x^3 dx = (8/4)x^(3+1) = 2x^4For -x^2: ∫(-x^2) dx = (-1/3)x^(2+1) = -(1/3)x^3For 5x: ∫5x dx = (5/2)x^(1+1) = (5/2)x^2For -1: ∫(-1)dx = -xPutting them all together:∫(8x^3 - x^2 + 5x - 1)dx = 2x^4 - (1/3)x^3 + (5/2)x^2 - x + CHere C is the constant of integration, which arises because integration is an indefinite integral.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com