For each K=0,1,2,3,... find a function Fk(X) such that (Fk)'

[Tuugii]

I'm having problems to understand following problem:

For each K = 0, 1, 2, 3, ... find a function Fk(X) such that (Fk)'(X) = X^K.

What does this mean?

thanks a lot,
Tuugii

 

[pka]

Re: help me!!!

For each K=0,1,2,3,... find a function Fk(X) such that (Fk)'(X)=X^K, what does this mean??…

Without a full and complete statement of the problem, it is impossible to give a correct answer. It may mean that
\(\displaystyle \L\left( {F_k } \right)'(x) = x^k \quad \Rightarrow \quad F_k \left( x \right) = \frac{{x^{k + 1} }}{{k + 1}},\quad F_k (0) = 0\).