Question

Find the most general form of the antiderivative, f(x) , of the function f(x)=8x32−6x14 .

A. f(x) = 8x⁴ - 6x¹4 + C
B. f(x) = 8x³ - 6x¹4 + C
C. f(x) = 8x³ + 6x¹4 + C
D. f(x) = 8x⁴ - 6x¹4 - C

Answer 1

To find the most general form of the antiderivative of the function f(x) = 8x^3 - 6x^14, we can use the power rule for integration.

Step-by-step explanation:

To find the most general form of the antiderivative, we can use the power rule for integration. According to the power rule, the antiderivative of x^n is (1/(n+1))x^(n+1) + C, where C is the constant of integration.

Applying the power rule to the function f(x) = 8x^3 - 6x^14, we can write the antiderivative as (8/(3+1))x^(3+1) - (6/(14+1))x^(14+1) + C.

Simplifying this expression, we get the most general form of the antiderivative as f(x) = 2x^4 - (6/15)x^15 + C.