Question

Question #b0c52

Answer 1

You need to find the constant!

Explanation:

I think you have a typo: you mean `2/9(x^3+1)^{3/2}`.

Anyway, the trick is that `f(x)` is AN antiderivative, so `f(x)=2/9(x^3+1)^{3/2} + C` where `C` is a real number such that `f(2)=0`. So, in order to find `C`, we have that

`2/9(2^3+1)^{3/2} + C=0 Rightarrow C=-6`.

Hence `f(x)=2/9(x^3+1)^{3/2} -6`, so `f(0)=2/9-6=-10/9`