Consider the function f ( x ) = 6/x^2 - 8/x^6.

Question

Consider the function

6 8

f(x)= — – —

x² x⁶

Let F(x) be the antiderivative of f(x) with F(1)=0.

Then F(x)= _____

Answer 1

Since F(x) is antiderivative of f(x),

F(x) = -6/x + 8/(7x^7) + C

Now, plug in 1 for x and 0 for F(x).

0 = -6 + 8/7 + C

C = 34/7

Thus, F(x) = F(x) = -6/x + 8/(7x^7) + 34/7