Question - Integration of Polynomial
mathintegration of polynomialintegral of polynomialantiderivative of polynomialpolynomial integration
Solution:
The given integral is:∫ (8x^3 - x^2 + 5x - 1) dxTo solve this integral, we integrate each term of the polynomial separately:∫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 = -xCombining the integrated terms gives us the antiderivative:2x^4 - x^3/3 + 5x^2/2 - x + Cwhere C is the constant of integration.
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