Question - Definite Integrals of Polynomial Functions
Solution:
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^42. ∫(-x^2) dx = -(1/3)x^33. ∫5x dx = (5/2)x^24. ∫(-1) dx = -xNow, putting it all together:∫(8x^3 - x^2 + 5x - 1) dx = 2x^4 - (1/3)x^3 + (5/2)x^2 - x + CWhere C represents the constant of integration.
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