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## Homework Statement

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) = ∫**

_{0}^{x}sin(t^2)dt## Homework Equations

R

_{n}= 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