Example Question - integral solvers

Definite Integrals of Polynomial Functions

The image shows an integral which needs to be solved. The function to be integrated is a polynomial: 8x^3 - x^2 + 5x - 1. To solve the integral, we need to integrate each term individually with respect to x. Here's how you integrate each term: 1. ∫8x^3 dx = (8/4)x^4 = 2x^4 2. ∫(-x^2) dx = -(1/3)x^3 3. ∫5x dx = (5/2)x^2 4. ∫(-1) dx = -x Now, putting it all together: ∫(8x^3 - x^2 + 5x - 1) dx = 2x^4 - (1/3)x^3 + (5/2)x^2 - x + C Where C represents the constant of integration.