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im not sure where to go from there

then \[f(c _{k}) = 2*k^2 *\Delta x ^3 + k*\Delta x^2 + 3 \Delta x\]

and \[S _{n} = 2 \Delta x ^3 \sum_{}^{} k^2 + \Delta x^2 \sum_{}^{} k +3 \Delta x\]

you got it from here?

yea i think so i think what confuses me the most is 3+(-3k/n)

do what I did before you sub.s in 'delta x = b/n'

start at x=0... move delta x to the right... what's the height of the rectangle you'd draw there?

|dw:1354238714258:dw|

|dw:1354238854668:dw|

so the sum of areas is going to look like:
(2*(k*delta x)^2 + k*delta x +3)*delta x

2*k^2*(delta x)^3 + k*(delta x)^2 +3*delta x

summing from k=1 to n

that's the sum I wrote above

oh alright, thanks i appreciate the help!

does that make sense?

Yeah it does, im trying to work through the problem. ill have an answer soon enough though

still there?

I didn't write the last term on the summation properly

it should be:\[\Delta x \sum_{k=1}^{n} 3\]

oh ok, thats makes more sense now

Its either 0 or -6 i think 0 because n = 3, am i correct?

it's -63/2