Question - Integration of Polynomial Function
mathindefinite integralpower rule for integrationintegration of polynomial functionpolynomial function integration
Solution:
Certainly! You need to integrate the given polynomial function with respect to x. The integration of a polynomial function is done term by term. Here are the steps:Given function: ∫(8x^3 - x^2 + 5x - 1)dx1. Integrate each term separately using the power rule for integration: ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.For the first term 8x^3:∫8x^3 dx = 8 * (x^(3+1))/(3+1) = 8 * x^4/4 = 2x^4For the second term -x^2:∫(-x^2) dx = - (x^(2+1))/(2+1) = -x^3/3For the third term 5x:∫5x dx = 5 * (x^(1+1))/(1+1) = 5/2 x^2For the fourth term -1:∫(-1) dx = -x2. Combine the integrated terms and include the constant of integration:2x^4 - (1/3)x^3 + (5/2)x^2 - x + CTherefore, the indefinite integral of the given function 8x^3 - x^2 + 5x - 1 with respect to x is:2x^4 - (1/3)x^3 + (5/2)x^2 - x + C
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