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jennychan12
 2 years ago
Integral Question.
See below,
jennychan12
 2 years ago
Integral Question. See below,

This Question is Closed

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0If \[\int\limits_{0}^{6} (x^22x+2)dx\] is approximated by 3 inscribed rectangles of equal width, then the approximation is... 1) 24 B) 26 C) 28 D)76 E) 48

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0sorry typed something wrong. and that 1 is supposed to be an A

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0so i got the integrated area to be 48, so answers either a b or c

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Wait, what kind of rectangles? Left, right, or midpoint?

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0the problem doesnt say. i'm assuming left

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0cuz it says inscribed

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Well you are right. It's either A, B or C :D . Now can you do it out? :) .

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1\[\Delta(x)=\frac{ 60 }{ 3 }\]

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0i'm confused my friend says to use riemann sum. what's the formula for that?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1In this particular example, a Riemann sum is basically the sum of the individual rectangles.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1When you learn about definite intergals you will have a good idea about what they actually mean.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0is it \[\frac{ ba }{ n } \sum_{i = 1}^{n} f(x) \] ??

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1So yeah you get the idea. It's the sum of all the rectangles multiples by the change in x,(i.e the width) .

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0that's what i did but i got 28 and the answer's 26

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Then you have to use diffrent kinds of rectangles because your answer is correct.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But if you use left rectangles then it's 28.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0why? sorry can u explain?

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0so right hand it's 26 or..?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1So this is a very stupid question because it dosen't specify the type of rectangles.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Well right hand is 76 actually.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But it dosen't specify what type of rectangle. Left, right or midpoint.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0where'd the 26 come from? midpoint?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But shall I explain left and right rectangles?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1If you use left, you get 28. If you use right you get 76.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0wait so where did the 26 come from. please explain. i'm so lost. :(

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.126 isn't the correct answer.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0cuz this other person used 2(f(1)+f(2)+f(4)) and got 26 but i don't understand where the f(1) came from...

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, 28 should be correct. I disagree with the answer.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1If you use 3 subintervals you CANNOT get 26 in anyway.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1The formula would be (2)(f(0)+f(2)+f(4))

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i did that... and got 28

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Which is absolutely correct.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1It CANNOT be 26 if you use left rectangles.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1if you use right rectangles it's (2)(f(2)+f(4)+f(6)) which is 76.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i got 28 and 76 but i chose 28. so my teacher is wrong. hmph.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Yep, you teacher is wrong.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0thanks for clarifying. :)

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1In reality the exact value of that integral is 48 but you will learn that later.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i know. i calculated it.

yun2thejae
 2 years ago
Best ResponseYou've already chosen the best response.1Good 'ol Riemann's screwing with everybody's head.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1I just hope I don't have to do it after my first year in uni :/ . AP calc helped so much though XD .

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0ohhhhhhh i think i got it they used average value

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1$$A\simeq2(2^22(2)+2+4^22(4)+2+6^22(6)+2)\\\ \ \ =2(44+2+168+2+3612+2)\\\ \ \ =2(38)=76$$ (using right endpoints)$$A\simeq2(0^22(0)+2+2^22(2)+2+4^22(4)+2)=2(2+44+2+168+2)\\\ \ \ =2(14)=28$$ (using left endpoints)$$A\simeq2(1^22(1)+2+3^22(3)+2+5^22(5)+2)\\\ \ \ =2(12+2+96+2+2520+2)\\\ \ \ =2(13)=26$$ (using midpoints)

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1^ Reason why they they should specify the question.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0my friend just assumed that inscribed meant left end points

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1@oldrin.bataku : Please don't just give the answer next time. The point of this place is to help other people learn. Not give them the answer.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1@jennychan12 : That's a flase assumption.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1@oldrin.bataku : If you use midpoints, it's 46 not 26.

yun2thejae
 2 years ago
Best ResponseYou've already chosen the best response.1Lol Oldrin and i have been spending plenty of time explaining problems to different users. I would give him a break xD. I was bored and decided to use this site for the first time today and, oddly enough, I can't stop attempting to solve problems. Probably because I don't want to forget my math whilst im on winter break.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1I know but it's just that's it's against the TOS so I try not to. I make that mistake too. It's cool ^_^ .

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1@Dido525 you're right, 2(5) = 10 so it's actually 2(23) = 46 for the approximate area.

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1If it requires inscribed rectangles then the approximation must use left endpoint... mid and right will not be entirely under the parabola.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1That's why we have the trapozoidal rule ;) . Ans simpsons rule :P .

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But yes @oldrin.bataku is correct. If they MUST be inscribed then you MUSt use left rectangles.

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1@Dido525 if you go into a Scientific Computation course you'll learn about plenty more numerical methods e.g. RungeKutta or AdamsMoulton :p Euler's and Verlet are really common for physics problems.

yun2thejae
 2 years ago
Best ResponseYou've already chosen the best response.1Conversation is too much for this PoSci major xD.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1I looked at Rungekutta but it makes no sense XD . I am going much deeper into math next year so hopefully then :) .

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Sorry that we turned this page into a discussion @jennychan12 .

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1Nobody drew a damn diagram :P

yun2thejae
 2 years ago
Best ResponseYou've already chosen the best response.1Diagram was drawn in the other thread.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0if u wanna see http://openstudy.com/study#/updates/50d15940e4b069abbb70d3c0

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1that's the same thread as this one...

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1355899651047:dw That would be incorrect since it does not enclose the curve.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i got really confused and tried to do another one to resolve my confusion... :D cuz that other person made me confused

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1355899646424:dw

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1If you use midpoints it still dosen't enclose the curve fully.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1Inscribed rectangles *should* mean rectangles within the curve, but it sounds like that didn't work, so the damn question is broken.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1It's is 28 though without a doubt.

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1More than likely your teacher made an error.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1inscribed rectangles would give 26, but i feel like that was already covered in this mess somewhere

yun2thejae
 2 years ago
Best ResponseYou've already chosen the best response.1You haven't done "work" problems in your calc class yet have you?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1Wait, why isnt the answer 26? 3 inscribed rectangles = area of 26.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0what do u mean? kinetic energy? i do that in physics....

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0@agent0smith can u explain???

yun2thejae
 2 years ago
Best ResponseYou've already chosen the best response.1there are "work" problems you use calculus for. Pray that you do not have to do them xD

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1If you use 3 inscribed rectangles it's 28 not 26.

yun2thejae
 2 years ago
Best ResponseYou've already chosen the best response.1The previous thread came up with 26. this one says 28. let's meet half way and say it's 27...oh wait.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1The height of the first is 1, length is 2 height of the second is 2, length is 2 height of the third is 10, length is 2. 2+4+20

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1How'd you get 28, @Dido525

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0left endpoint is 28

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1=(2) * ( f(0) + f(2) + f(4) ) = (2) * ( 2 + 2 + 10 ) = 28

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1Inscribed have to be all within the curve, no edges jutting out: it's not f(0), it's f(1), the height of the first rectangle.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1That is not an inscribed rectangle.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0that's what that other person did in that other thread 2(f(1)+f(2)+f(4)) = 26 but why would be f(1)??? where does the 1 even come from?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1I'll draw it jenny. One sec.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1I want to see this too.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1dido, look at the graph: http://www.google.com/search?q=x%5E22x%2B2&aq=f&oq=x%5E22x%2B2&sugexp=chrome,mod=18&sourceid=chrome&ie=UTF8 and then look where a rectangle at f(0) would fall... it's not inscribed. it goes over the curve.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Isn't that the same thing as inscribed?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Inscribed meaning within.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1No, inscribed means it falls completely within the curve, no jutting out over it.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0okay. i understand that f(1) = 1 but.... oh wait. i see where you're going with this....

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But rectangles will never cover a curve fully, it's impossible.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Like, it covers it fully but it's an overestimate.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1Those are inscribed rectangles, they underestimate the area greatly of course.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Ahh, NOW this makes sense.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But if it's an underestimate, it's not inscribed is it?

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0ok yeah i see it too.

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1I googled inscribed rectangles just to be sure.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Wait, why did you do a midpoint for the first rectangle?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1Because that's the only way to have it inscribed. http://en.wikipedia.org/wiki/Inscribed_figure

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1NOW this all makes sense :D .

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1Inscribed rectangles can be either left or right endpoint

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1@jennychan12 you see how it's 26 now? the height of the first is f(1), next is f(2), then f(4)

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1I would give you my medal if I could :P .

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1haha :) this whole confusion was all over the meaning of the word inscribed :D

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Agreed! :D . But hey, this might be n my final so it was good for me too :) .

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1haha good :) hopefully this clears things up Jenny, before you went and told your teacher he/she was wrong because a bunch of people on the internet said so! :D

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1@jada1701877 : You should have given that to agent.

jennychan12
 2 years ago
Best ResponseYou've already chosen the best response.0thanks so much! and yeah, i went off at like 11 cuz i went to sleep. :)
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