Question #b0c52

1 Answer
Apr 17, 2017

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