a. Suppose that f is bounded on [a, b], and that a is a function such that integral from [a b] of f exists. We will show directly that the integral from [a b] of f^2dα exists exists.

Let P be a partition of [a, b], and let M and m be the maximum and minimum, respectively of f on [x, x]. Then
U(f, p, ) – L(f, P, ) =

, where M = _______

Explain how this implies that the integral from [a b] of f^2dα exists

(5 points) b. If the integral from [a b] of f2dα exists does it follow that integral from [a b] of f exists? Prove this or give a counter example.

2. Originally Posted by abk6690
a. Suppose that f is bounded on [a, b], and that a is a function such that integral from [a b] of fexists. We will show directly that the integral from [a b] of f^2dα exists exists.

Let P be a partition of [a, b], and let M and m be the maximum and minimum, respectively of f on [x, x]. Then
U(f, p, ) – L(f, P, ) =

, where M = _______

Explain how this implies that the integral from [a b] of f^2dα exists

(5 points) b. If the integral from [a b] of f2dα exists does it follow that integral from [a b] of fexists? Prove this or give a counter example.

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