Maclaurin series and radius of convergence

Question

Find the maclaurin of f(x)= ∫ (from 0 to x) t² e^(t)² dt and find its redius of convergence

 

I dont understand what the integral means ? 

Answer 1

You should have a theorem in your text book indicating that for x n the radius of convergence you can find MacLaurin for f(t) in this case t2et^2, then integrate that series term by to get a power series representation for the integral in question. The assumption here is that you know how to find the MacLaurin series and radius of convergence for f(t). Get that and then integrate term by term.

Answer 2

To determine an expression for f(x), you can antidifferentiate, using Integration by Parts, I think.