Answer :
The general antiderivative of the function [tex]f(x) = 8x^9 + 4x^5 - 4x^2 - 10[/tex] is [tex]F(x) = (8/10)x^10 + (4/6)x^6 - (4/3)x^3 - 10x + C[/tex], where C is the constant of integration.
To find the antiderivative of f(x), we integrate each term separately. The antiderivative of a monomial [tex]x^n[/tex] is given by [tex](1/(n+1))x^(n+1)[/tex], and for a constant term, it is simply the term multiplied by x. We can write the antiderivative of f(x) as F(x) = [tex](8/10)x^10 + (4/6)x^6 - (4/3)x^3 - 10x + C[/tex], where C represents the constant of integration.
In the first term, 8x^9, we add 1 to the exponent and divide the coefficient by the new exponent: [tex](8/10)x^10[/tex]. Similarly, for the second term,[tex]4x^5, we integrate it to (4/6)x^6.[/tex]For the third term,[tex]-4x^2[/tex], we add 1 to the exponent and divide the coefficient by the new exponent: -[tex](4/3)x^3.[/tex] The constant term, -10, integrates to -10x. Finally, we add the constant of integration, C, to account for the fact that the derivative of a constant is zero.
Therefore, the general antiderivative of [tex]f(x) = 8x^9 + 4x^5 - 4x^2 - 10[/tex] is [tex]F(x) = (8/10)x^10 + (4/6)x^6 - (4/3)x^3 - 10x + C[/tex], where C is the constant of integration.
Learn more about antiderivative here:
https://brainly.com/question/30764809
#SPJ11
