# Find Taylor series expansion and convergence radius for $\int_0^x\cos(\sqrt{t}\ )dt$

i must find the the Taylor series expansion (i've been asked not necessarily calculating it directly) and the convergence radios for this function :

$$f(x) = \int_0^x \cos(\sqrt{t}\ ) \, dt$$

I am new to this field, and im not really sure what do i need to do, so maybe this is an elementary question, but i'd appreciate it if you add explanations so i can understand.

Thanks alot.

Hint: to find the Taylor series expansion for this function, find the Taylor series expansion for $\cos(\sqrt{t})$, and then integrate it from $0$ to $x$.