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Integrate the following function both analytically and numerically. For the numerical evaluations use

(a) A single application of the trapezoidal rule,

(b) Simpson’s 1/3 rule,

(c) Simpson’s 3/8 rule,

(d) Boole’s rule,

(e) The midpoint method,

(f) The 3-segment-2-point open integration formula, and

(g) The 4-segment-3-point open integration formula. Compute percent relative errors for the numerical results.

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