Let f [0, 2] [0, ) be continuous and monotone increasing, with f(1) = 1. (A)...

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Let f [0, 2] [0, ) be continuous and monotone increasing, with f(1) = 1. (A) Point out one reason why f is integrable. (B) Write down the definition of the lower sum sy of f with respect to a partition F := (x0, x1,...,xn) of [0, 2], and deduce that, in our situation, SF = =1 f (xi1) (xi Xi1). - (C) Use the formula in (B) to prove that f f(x) dx 1. (D) Is f f(x) dx > 1? Justify your answer. (E) Is f f(x) dx > 1.01? Justify your answer. Let f [0, 2] [0, ) be continuous and monotone increasing, with f(1) = 1. (A) Point out one reason why f is integrable. (B) Write down the definition of the lower sum sy of f with respect to a partition F := (x0, x1,...,xn) of [0, 2], and deduce that, in our situation, SF = =1 f (xi1) (xi Xi1). - (C) Use the formula in (B) to prove that f f(x) dx 1. (D) Is f f(x) dx > 1? Justify your answer. (E) Is f f(x) dx > 1.01? Justify your answer.