Question: let 0 1 x a r c t a n ( x ) d x (a) Find the Taylor polynomial of order 2, P2(x), about

let

01xarctan(x)dx

(a) Find the Taylor polynomial of order 2, P2(x), about x=0 for the function arctan(x).

(b) Use Lagrange's formula for the remainder R2(x)=arctan(x)-P2(x) to show hat

01xarctan(x)dx01xP2(x)dx91

(c) Hence calculate I with an error up to 1/9.

(a

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