here is my problem: find the upper and lower sums for the region bounded by the graph of [tex]f(x) = x^2[/tex] and the x-axis between x=0 and x=2. I understand what this problem is asking but i don't understand how to compte the left and right endpoints. the left endpoint is the following:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]m_{i}=0+(i-1)\frac{2}_{n}[/tex] = [tex]\frac{2(i-1)}_{n}[/tex]

and the right enpoint is given as this:

[tex]M_{i}=0+i\frac{2}_{n}[/tex] = [tex]\frac{2i}_{n}[/tex]

The lower sum ( left enpoint) is the following:

8\3 - 4\n + 4\3n^2

and the right endpoint is computed in a similar fashion.

my question is, how do i find the left and right enpoints? what is the formula for doing this? what if the lower bound is not zero but some other number, how would i find it then?

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# Finding upper and lower sums of a region

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