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## Homework Statement

This is am example from my textbook

[tex] \int_{1}^{3} x^2 dx = 26/3 [/tex]

It then goes to define the arbitrary partition in [1,3] and maximum / minimum for each subinterval blah blah.. then it says

For each index i, 1 <= i <= n,

[tex] 3x_{i-1}^2 \leq x_{i-1}^2 + x_{i-1}x_i + x_i^2 \leq 3x_i^2 [/tex]

## Homework Equations

## The Attempt at a Solution

I'm totally lost about this.. why are the min / max of the interval multiplied by 3? How did the middle part get like that?

I've seen the last example of the identity function f(x) = x they can get a midpoint between the min / max then work with that.. but this is not the same.