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CalcDerp102
Group Title
Im doing a problem at the moment and im stuck its a right riemann sum problem, equation and how far i got posted below
 one year ago
 one year ago
CalcDerp102 Group Title
Im doing a problem at the moment and im stuck its a right riemann sum problem, equation and how far i got posted below
 one year ago
 one year ago

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CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits_{3}^{0} (2x^2 + x +3) dx\] \[\Delta x = 3/n\] \[x_{k} = 3 + 3k/n\] \[f(x_k) = (3+ 3k/n)^2  (3 + 3k/n) +1\]
 one year ago

CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
im not sure where to go from there
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
I think you'd be better off using: \[\huge \int\limits_{a}^{b} f(x) dx = \int\limits_{b}^{a} f(x) dx\] at the start
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
then \[f(c _{k}) = 2*k^2 *\Delta x ^3 + k*\Delta x^2 + 3 \Delta x\]
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
and \[S _{n} = 2 \Delta x ^3 \sum_{}^{} k^2 + \Delta x^2 \sum_{}^{} k +3 \Delta x\]
 one year ago

CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
so if be better of making the original equation negative then using that formula to find the equation
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
a bit easier, yes... that's probably why they gave it to you in the form that they did... so you could make the easy simplification
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
you got it from here?
 one year ago

CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
yea i think so i think what confuses me the most is 3+(3k/n)
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
do what I did before you sub.s in 'delta x = b/n'
 one year ago

CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
\[2 * (3+ \frac{ 3k }{ n }^2) * \frac{ 3 }{ n }^3 + (3+ \frac{ 3k }{ n }) * \frac{ 3 }{ n } + 3\frac{ 3 }{ n }\] is this what im looking for or do does k = 1
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
start at x=0... move delta x to the right... what's the height of the rectangle you'd draw there?
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
dw:1354238714258:dw
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
height is f(delta x) width is delta x area is f(delta x) * delta x which is (2*(delta x)^2 + delta x +3))*delta x
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
dw:1354238854668:dw
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
next step: go another 'delta x' to the right height is 2*(2*delta x)^2 + 2*delta x +3 width is delta x area is (2*(2*delta x)^2 + 2*delta x +3)*delta x
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
so the sum of areas is going to look like: (2*(k*delta x)^2 + k*delta x +3)*delta x
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
2*k^2*(delta x)^3 + k*(delta x)^2 +3*delta x
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
summing from k=1 to n
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
that's the sum I wrote above
 one year ago

CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
oh alright, thanks i appreciate the help!
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
does that make sense?
 one year ago

CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
Yeah it does, im trying to work through the problem. ill have an answer soon enough though
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
still there?
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
I didn't write the last term on the summation properly
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
it should be:\[\Delta x \sum_{k=1}^{n} 3\]
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
so\[S _{n} = 2(\Delta x)^3\sum_{k=1}^{n} k^2 + (\Delta x)^2 \sum_{k=1}^{n} k +\Delta x \sum_{k=1}^{n} 3\]
 one year ago

CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
oh ok, thats makes more sense now
 one year ago

CalcDerp102 Group TitleBest ResponseYou've already chosen the best response.0
Its either 0 or 6 i think 0 because n = 3, am i correct?
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
it's 63/2
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
n is the number of divisions in the partition... you find the sum above (in terms of n) ... you sub.s in b/n for delta x and then you take the limit as n>infinity
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
then use b=3 (the interval length) and finally, make the whole result negative ( due to the simplification we did at the very beginning)
 one year ago
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