.1.

2 2. Since it is difﬁcult to evaluate the integral / 812 d1: exactly, we will approximate it using Maclaurin

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polynomials. (a) Determine P4(:1:), the 4th degree Maclaurin polynomial of the integrand 332. (b) Obtain an upper bound on the error in the integrand for :r: in the range

0 S x S 1/2, when the integrand is approximated by P4 (:13). (c) Find an approximation to the original integral by integrating P4(:1:).

((1) Obtain an upper bound on the error in the integration in (c).

(e) Use MATLAB to verify your calculation in (a). Math