Using Taylor series, Find a polynomial p(x) of minimal degree that will approximate F(x) throughout the given interval with an error of magnitude less than 10-4
F(x) = ∫0x sin(t^2)dt
Rn = f(n+1)(z)|x-a|(n+1)/(n+1)![/B]
The Attempt at a Solution
I am confused about the integral and have never done a problem like this
Do I use the fundamental theorem of calculus to solve the nth derivative of the function and see at what point the error is below the required value?
Do I somehow integrate the taylor series for sin(x) and somehow use that?
I just do not know how to go about this problem