1. (a) Evaluate the limit Σk: k=1 by expressing it as a definite integral, and then evaluating the definite integral using the Fundamental Theorem of Calculus. (b) Evaluate the integral = lim n→∞ n(n+1) 2 0 by firstly expressing it as the limit of Riemann sums, and then directly evaluating the limits using the some of the following formulae: " k=1 π COS(™) n n Σk² = Σκ k=1 (x − x²) dx n(n + 1)(2n + 1) 6 7 n Σk k³ k=1 2 - (n(n + 1)) ². = 2

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