Consider the function
f(x)=(8)/(x^2)−(8)/(x^5)
.
Let F(x) be the antiderivative of f(x) with F(1)=0.
Then F(2) equals ?
F = ∫ 8/x^2 - 8/x^5 dx
= 8/3 x^3 - 8/6 x^6 + C
Since F(1) = 0,
8/3 x^3 - 4/3 x^6 + C = 0
C = 4/3 - 8/3 = -4/3
F(x) = 8/3 x^3 - 4/3 x^6 - 4/3
F(2) = 8/3 (8) - 4/3 (64) = -64