Question

Consider the function f(x)=(7/x^2)-(6/x^6).
Let F(x) be the antiderivative of f(x) with F(1)=0.
Then F(2) equals _____.

Answer 1

Write it as
f(x) = 7x^-2 - 6x^-6
F(x)= -7x^-1 + (6/5)x^-5 + c

F(2) = -7/2 + (6/5)/2^5 + c
= ......

Answer 2

since F(1) = 0, we have
-7 + 6/5 + c = 0

which you can plug in to evaluate F(2)