A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Find the value of the following definite integral using the limit of a Riemann sum, and express as a common fraction. You should use the formulas for ∑i, ∑i^2, and ∑i^3 given in class.
S(Integral from 2 to 1) (x^33x)dx
anonymous
 5 years ago
Find the value of the following definite integral using the limit of a Riemann sum, and express as a common fraction. You should use the formulas for ∑i, ∑i^2, and ∑i^3 given in class. S(Integral from 2 to 1) (x^33x)dx

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The actual question is attached

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i attached the actual question

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i see it... so what are the 3 summation formulas?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me get them from my notes

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0if I recall correctly, the Reiman limits are just taking the area of slices as the thickness of dx goes to zero right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes and i she didnt give us the formulas even though she said she did, let me check the book.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(f(x+dx)  f(x)) dx; we could also take the "average height" between f(x+dx) and f(x)...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0dx just stands for delta x, any arbitrary number... where dx = (ba)/n... any of this make sense?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0dx = (12)/n = (1+2)/n = 3/n

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, them pictures is what I said lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the limit as n> inf......

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so then I got lim as n goes to infinity of the summation [(2+3i/n)^33(2+3i/n)](3/n)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0need to work out something like this right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea but that one is less complicated haha

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol .... use the Esummation for the cubic function

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the answer we are going for is 3/4 for reference

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is my first step correct?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we can split the addition up into to parts just like regualr integration, because regular integration is the result of this reimann sum stuff, so do x^3 and x sepertaely

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0[E] x^3 dx  [E] 3x dx the 3 can move out [E] x^3 (3/n)  3 [E] x (3/n)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{n \rightarrow \infty}\sum_{i=1}^{n}[(2+3i/n)^33(2+3i/n)](3/n)\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0im lost on what that (2+3i/n) stuff means, help me out :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its part of the reimann sum

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the formulas we have to use, that is the n^3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{} x^{3}(3/n) 3 \sum_{}x(3/n)\] is whats in my head

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well the integral is \[\int\limits_{2}^{1}(x^33x)dx\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, and the reiman is proof that we can split that into 2 parts right? \[\int\limits_{} x^3 dx 3\int\limits_{}x dx\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0∑ x^3 (3/n)−3 ∑ x (3/n) is its equivalent, tell me if im wrong... but whats our next step after this?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets work each one on its own...ok

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and thats what i showed above

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0as one complete summation multiplied by 3/n

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you say "plug in" but i have no idea how that happens, im pretty much an idiot when it comes to the limit stuff, show me step by step please how we "plug in" to get: lim n→∞ ∑ i=1 n [(−2+3i/n)^3 −3(−2+3i/n)](3/n)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i need to break it even further for you

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol.... well, I got that part :) How do we move from that to the "formula for" [E] i^3 and [E] i I am not familiar with those formulas, yet :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its just pulling things out and taking individual summations, should i show you where i am so far?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yes please ∑ i^3 = (1/4)n4 + (1/2)n3 + (1/4)n2 is what I found online

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{n \rightarrow \infty}\sum_{i=1}^{n}3/n[8+12i/n+12i/n18i^2/n^2+12i/n18i^2/n^218i^2/n^227i^3/n^33(2+3i/n)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wow i guess my thing was too long, thats only half of it

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0:) heres what I found that helps me out

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok that works, lets start over then from 3/n being delta x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0since 3/n = delta x, we simply multiply that to x^3? to get: 3(x^3)/n ?? is that right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmm sure, keep going because i wont know where you are going till you go further

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[3\sum_{n=1}^{\infty} (x^3)/n\] Does this look right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lol ....if it dont look right, then why should I keep going :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0im trying to make sense of where you are going

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0....... you gotta drive some of the way, im lost here for the moment

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh k , im trying to think...problem is i cant find the equation that would help you

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how i formulated the entire sum?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0A=lim_{N→∞}Δx∑_{j=1}^{N}f(a+jΔx)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yup.... im still at the split and trying to apply the formula for [E] x^3 to the left part. the top part of the [E] is gonna be (ba) right? which we determined to be 3.... but its not sinking in....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ok....so delta x is a constant that gets pulled out to the left ... am I seeing that right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but you see how the i is appearing now. In the equation, it names it j, but the common known term is i

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0and the "i" is simply each iteration of the sums....right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the integral should =3/4 after the long process, im trying to get through all the steps

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yeah....when i read over that reaimann stuff I gloosed at it and figured, its true, so why do it the long way :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol cause my professor doesnt want to make life easy

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(a + i /x\) the i is each iterations from 1 to infinity. is the a the same as in our ba interval?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0limn→∞∑i=1n[(−2+3i/n)3−3(−2+3i/n)](3/n)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(2 + 3i/n) is a standard interation then, is that correct?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dont forget the cubed

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0is the "n" from 3/n is the one we are limiting to infinity right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey if you dont wanna type the dumb sigma and lim n thing, just say lim and sigma, ill know what you are saying or use the equation feature on here

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dumb summation sign i mean*

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0n[(−2+3i/n)3−3(−2+3i/n)](3/n) this is you combining the terms together right??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the n in front shouldnt be there that was part of the format for the summation

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ok...... (sigma) (2 +3i/n) (3/n) is the right term then correct?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0summation but yes that is correct

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0isnt it 3(2 +3i/n) (3/n)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{} (2+3i/n) (3/n)\] would be the \[\sum_{} x \] formula part right? the 3 part of the 3x doesnts need to be included in this process if i recall correctly

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0im pretty sure you do because its part of the integral function

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but if you are confident, you understand this better then me so ill take your word for it

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{?}^{?} 3x = 3\int\limits_{?}^{?}x \rightarrow3 x^2/2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well you are going to have a 8 from the cube equation so its better if you keep everything together when you distribute it right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i guess it doesnt matter go ahead, you sound excited because i think you understand it now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do your thing, ill just learn from you

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0keep this split up, dont try to solve it all as one summation, work that parts.... use the formulas for [E]x and [E]x^3 seperately

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it still will work out taking as pieces?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum{}(2 +3/n)(3/n)\] fits into n(n+1)/2 somehow, and yes, it will work easier and just as good if we split it up

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0think of it as the granny way of doing integrals; its actually proof that we can split integerals up and work them

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0forgot to pu an i in there :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok let me write step by step following you on actual paper

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we can split derivatives up and work them, integrals are just eh opposite of derivatives.....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0this computer is having a hard time keeping up with formating the "equation"editor stuff, can we start a new question post?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me make a new one

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0k go to the top of the question list
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.