a) Prove that for each n ∈ N,is a partition of [0, 1].b) Prove that a bounded function f i...

a) Prove that for each n ∈ N,

is a partition of [0, 1].

b) Prove that a bounded function f is integrable on [0, 1] if

in which case  equals I0.

c) For each of the following functions, use Exercise to find formulas for the upper and lower sums of f on Pn, and use them to compute the value of

α) f (x) = x

β) f (x) = x2

γ)

Exercise

Parts a) and c) of this exercise are used in Sections and. Prove that the following formulas hold for all n ∈ N.

a)

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b)

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c)

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d)