consider the function f(x)=4/x^2 -2/x^6. let f(x) be the antiderivative of f(x) with f(1)=0. Then f(5) equals

Answer 1

"let f(x) be the antiderivative of f(x) "
this makes no sense unless f(x) = e^x
so is f(x) the antiderivative or .... ?

suppose f ' (x) = f(x)=4/x^2 -2/x^6
= 4x^-2 - 2x^-6
then
f(x) = (-4x^-1) + (2/5)x^-5 + c
if f(1) = 0
-4 + 2/5 + c = 0, c = 18/5

f(x) = -4/x + (2/5) /x^5 + 18/5
f(5) = -4/5 + 2/15625 + 18/5 = 2.8