Evaluate the following integral:

(a) Analytically;

(a) Single application of the trapezoidal rule;

(c) multiple-application trapezoidal rule, with n = 2 and 4;

(d) Single application of Simpson’s 1/3 rule;

(e) Multiple-application Simpson’s 1/3 rule, with n 4;

(f) Single application of Simpson’s 3/8 rule; and

(g) multiple-application Simpson’s rule, with n = 5. For each of the numerical estimates (b) through (g), determine the percent relative error based on (a).

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. (1 -e 2) dx