adanced calculus

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May 2010
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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.





 

mr fantastic

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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.
This question looks like it comes from work that counts towards your final grade. MHF policy is to not knowingly help with such questions. You can pm me and discuss this if you want. Thread closed.
 
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