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Express the limit as a definite integral over the indicated interval [a,b]
 one year ago
 one year ago
Express the limit as a definite integral over the indicated interval [a,b]
 one year ago
 one year ago

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bmelykBest ResponseYou've already chosen the best response.0
\[\lim n>0 \sum_{i=1}^{n} [2(1+\frac{ 2i }{ n }5]\frac{ 2 }{ n }\] over [1,2]
 one year ago

bmelykBest ResponseYou've already chosen the best response.0
lim as n approaches 0 * if that doesnt look clear. looking for a step by step explanation.
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
is it like this \[\huge \lim_{n \rightarrow 0} \sum_{i=1}^{n}[2(1+\frac{2i}{n})5]\frac{2}{n}\]
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
we want to express the sum as\[\huge \sum_{i=1}^{n}f(c_i)\Delta x\] where \[\Delta x=\frac{2}{n}\]
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
we also wanna find c_i as the endpoint of each interval, \[\huge c_i=\frac{2}{n}i\]this means that we have \[\huge \sum_{i=1}^{n}[2(1+c_i)5]\Delta x\]
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
hence you can steal your function easily from that f(x)=
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
\[f(x)=2(1+x)5=2x3\]@shubhamsrg @ParthKohli
 one year ago

bmelykBest ResponseYou've already chosen the best response.0
and is that the answer?
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
\[\int\limits_{1}^{2}2x3\]
 one year ago

bmelykBest ResponseYou've already chosen the best response.0
so then i integrate normally?
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
yes but did you understand
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
\[\Large \Delta x=\frac{ba}{n}=\frac{2(1)}{n}=\frac{3}{n}\]
 one year ago

bmelykBest ResponseYou've already chosen the best response.0
i subbed in the wrong number
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
\[x^23x {\huge}_{1}^{2}=4613=6\]
 one year ago

bmelykBest ResponseYou've already chosen the best response.0
so you're saying delta c is different than the other perosn?
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
i was thinking 3/n but its not even in the equation
 one year ago

bmelykBest ResponseYou've already chosen the best response.0
im sorry i have to go to class but i will be back so please continue to explain further, thank you and chat soon
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
are you sure the class is {1,2} not {0,2}
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
so we should write\[\frac{1}{3}\sum_{i=1}^{n}[2(32\frac{3i}{n})5]2\frac{3}{n}\]
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
also 5(3) \[f(x)=\frac{2}{3}[2(32x)15]\]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
\[\left[2\left(1+2\frac{i}{n}\right)5\right]\Delta x=\left[2\left(1+\frac{2}{3} \frac{3i}{n}\right)5\right]\frac{2}{3}\frac{3}{n}\Delta x\] \\[f(x)=\frac{2}3{}\left[2\left(1+\frac{2}{3}x\right)5\right]\]
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
left side is stated as this correct? \[\lim_{n\to0}~\sum_a^b~f(a+i\frac{ba}{n})\frac{ba}{n}~;~i=0,1,2,...,b\frac{ba}{n}\]
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
gpt me i parts mixed around, and put abs in the wrong place, that summation
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
hmm interval (1,2) then ba= 21 = 3 so there seems to be a little confusion unless we are spose to factor within the given summation fo accomodate that
 one year ago

KatClaireBest ResponseYou've already chosen the best response.0
@bmelyk @jonask it's [1,3], you typed it in from another question wrong
 one year ago

KatClaireBest ResponseYou've already chosen the best response.0
@amistre64 @sirm3d ^
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
so is it [1,2] or [1,3]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
then it's just \[\Large \int_1^3 (2x5)\;\mathrm dx\]
 one year ago
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