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#