Final answer:
The antiderivative of the function f(x) = 5x^2 - 8x^6 is ( -5/3x^3 + 2/7x^7 + C).
Step-by-step explanation:
The antiderivative of the function f(x) = 5x^2 - 8x^6 is ( -5/3x^3 + 2/7x^7 + C), which corresponds to option b. (frac5x - frac2x^5 + C). To find the antiderivative, we can use the power rule for integration, which states that the antiderivative of x^n is (1/(n+1))x^(n+1). Applying this rule to each term of the function, we get (-5/3x^3) for the first term and (2/7x^7) for the second term. Adding the constant of integration C at the end gives us the final result.