The problem I'm having is using one of the Fundemental Theorems of Calculus to integrate the function with respect to in order to find my function. This specific function is fairly challenging for me to integrate. It is a beautiful problem and I will attempt to solve it.
Thanks for your input.
I think the point of this problem is you don't need to actually integrate the function because you can use FTCII to find f(1). What is f(1) if the integral of f(t) has bounds from 1 to 1?
From there, f'(a) is just f(t) and all further derivatives can easily be found. You don't need to find the integral of f(t) to write the Taylor polynomial of f(x).
Sorry I'm so late in responding to this but I just wanted to let you guys know that I completed the problem and I think I did very well on the test. I had to calculate a wicked third derivative of the function but I'm pretty sure I got the answer right.
Thanks for all your help!