f(x)= 0 if x=1/n for some n in the natural numbers,
and
f(x)=1 otherwise.
Show that f is integrable on [0,1] and the integral (with lower limit 0 and upper limit 1) of f = 1.
(hint: you have to create a partition of [0,1] as follows. Let epsilon>0 be given. One interval should have width epsilon/2 and contain the 'infinite tail end' of the sequence of points 1/n and the remaining intervals should contain the 'finite beginning' of the sequence 1/n and have total length epsilon/2. Now calculate U(f,P) and L(f,P), show that U(f,P) - L(f,P) = epsilon and argue that the given integral is true.)
I'm not very sure how to do this, even with the hint that follows.
Please help. thank you.
2007-04-03
23:44:17
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2 answers
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NeedHelpPlease
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Mathematics