1. The problem statement, all variables and given/known data Find the polynomal that approximates the integral of (t^2)e^-t^2 from 0 to x, [0,1], with an error less than 10^-3 2. Relevant equations You need to use taylor theorem & remainder estimation theorem 3. The attempt at a solution I set up the tailor series with the first 4 terms (1/e, 0, (2/e)(x-1)^2, (1/6)*(x-1)^4), but where am I supposed to go now? I integrated the series, but I still don't know if I got enough terms. Hell, what does it mean to integrate something from 0 to x? x isn't even a number! Does the book mean from 0 to 1, since t is an element between 0 and 1? Until I figure what the hell the book is on about, I can't use the remainder estimation theorem. I am extremely confused atm and I think the book I have is pretty bad at explaining.