Question: Please help answer this question on Newton-Cotes Integration: Let I = integral^2_1 x^2 ln x dx. a) Evaluate I exactly (by hand and with quad.

Please help answer this question on Newton-Cotes Integration:

Let I = integral^2_1 x^2 ln x dx. a) Evaluate I exactly (by hand and with quad. b) Use the midpoint rule with N = 10, 100, 1000 to obtain approximations of I. c) What value of N guarantees full accuracy (TOL = 5 times 10^-16)? Use Romberg extrapolation to obtain an accurate estimate of

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