(e) where 1. Asusme that f e C[a, bl. We would like to show that the midpoint rule has error 3 ba. We will do this in several steps. e (a, b) and h (a) Find, Tl (:r), the first order Taylor polynomial of f centered at and its remainder RI (:r). (b) To estimate Jab f (x) d:r, find Tl (x) dr. Show that this estimate gives the approximation from the Midpoint Rule. (c) To find the error of the Midpoint Rule, find fab RI (x) dr. You will need to apply the Weighted Mean Value Theorem for Integrals here. Simplify your answer in terms of h.