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any guesses for this one?

no guesses? i guess \(f(x)=x^2\)

on the interval \([0,1]\) divide the interval in to \(n\) parts each of length \(\frac{1}{n}\)

Just x^2?
I thought it had to be more than that though

then for each \(i\), \(f(\frac{i}{n})=\frac{i^2}{n^2}\)

oh wow! Dang. I hate this notation. It makes it ten times more complicated than it needs to be.

multiply each by \(\frac{1}{n}\) and add the up you get
\[\sum\frac{i^2}{n^3}\]

well don't be hoodwinked in to thinking these are all that easy
usually it is much harder to tell

I have another one a lot like this. with a sqaure root. but I'm not sure about it

interesting, because the i and n values would be different right?

because a-b / n ?