Question - Integral of a Polynomial Function
mathconstant of integrationpolynomial integrationintegral of polynomial functionintegrating polynomial equations
Solution:
The integral in the image is:∫ (8x^3 - x^2 + 5x - 1) dxTo solve the integral, integrate each term separately with respect to x:∫ 8x^3 dx = (8/4)x^4 = 2x^4∫ -x^2 dx = -(1/3)x^3 = -x^3/3∫ 5x dx = (5/2)x^2 = 5x^2/2∫ -1 dx = -xNow, combine the integrated terms:2x^4 - (1/3)x^3 + (5/2)x^2 - x + CHere, C is the constant of integration. The final answer for the integral is:2x^4 - (x^3/3) + (5x^2/2) - x + C
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