Upper and Lower Sums - Round Two (a) Consider the following partition sequences for the interval [0, 1]: Zn = (x0, x1, ..., xn), with xk = ½-½ Zn = (0, T1, T2, ..., Tn), with Ãk = 3 Determine the fineness measures | Z | and |Z❘ depending on n, as well as their limits for n → ∞, and justify why Zn is unsuitable for determining the integral. (b) Using the partition Z from (a), determine the integral So √x dx. Then slightly modify the partition and use it to determine the integral over the interval [0,6] for any bЄ R. Hint: You may use the summation formulas in this problem without proof: ΣΕ 1 k² = n(n+1)(2n + 1) and 1 k = n(n + 1).

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