(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The question is to use upper and lowers sums, U_{n}and L_{n}, on a regular petition of the intervals to find the integral from 1 to 2 of f(x) = [[x]], where [[x]] is the greatest integer function.

2. Relevant equations

[tex]\Delta[/tex]x = [tex]\frac{b-a}{n}[/tex]

3. The attempt at a solution

[tex]\Delta[/tex]x = [tex]\frac{2-1}{n}[/tex] = [tex]\frac{1}{n}[/tex]

The minimum and maximum of f(x) on every subinterval of [1,2] would be 1 except for the subinterval which includes x=2 where the maximum value of f(x)=2, so for f(x) there exists a unique number I such that L_{n}[tex]\leq[/tex] I [tex]\leq[/tex] U_{n}

I know that the area will be 1, as for [1,2) U_{n}= L_{n}= [tex]\Delta[/tex]x[tex]\sum[/tex]1 = [tex]\frac{1}{n}[/tex] x 1n = 1

However I am not sure how to include the subinterval that contains x=2 into my calculations. Any help on this would be great!

Thanks!

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# Homework Help: Use Upper And Lower Sums To Evaluate An Integral

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