Quiz 2 Problem 2. [10 points] Derive integrals that are closely-matching lower and upper bounds on the sum 1 In k k=n where n >3. Justify your answers with a diagram. Do not integrate. Your answers should be unevaluated integrals (a) Draw your diagram in the space below. To receive full credit, the diagram must clearly communicate why your integral bounds are correct Solution y In(n+1) n(2n) (b)Write your lower bound integral here ri- in( da (c)Write your upper-bound integral here 1Quiz 2 4 Problem 2. [10 points] Derive integrals that are closely­matching lower and upper bounds on the sum � 2n 1 ln k k=n where n ≥ 3. Justify your answers with a diagram. Do not integrate. Your answers should be unevaluated integrals. (a) Draw your diagram in the space below. (To receive full credit, the diagram must clearly communicate why your integral bounds are correct.) Solution. - 6 y = 1 ln x y = 1 ln(x 1 ln n 1 ln(n 1 n) +1) +1) ln(2 n − 1 n 2n � 2n 1 (b) Write your lower bound integral here → dx n−1 ln(x+1) � 2n 1 (c) Write your upper­bound integral here → dx n−1 ln x