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jennychan12Best ResponseYou've already chosen the best response.0
If \[\int\limits_{0}^{6} (x^22x+2)dx\] is approximated by 3 inscribed rectangles of equal width, then the approximation is... 1) 24 B) 26 C) 28 D)76 E) 48
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
sorry typed something wrong. and that 1 is supposed to be an A
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
so i got the integrated area to be 48, so answers either a b or c
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Wait, what kind of rectangles? Left, right, or midpoint?
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
the problem doesnt say. i'm assuming left
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
cuz it says inscribed
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Well you are right. It's either A, B or C :D . Now can you do it out? :) .
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
\[\Delta(x)=\frac{ 60 }{ 3 }\]
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
i'm confused my friend says to use riemann sum. what's the formula for that?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
In this particular example, a Riemann sum is basically the sum of the individual rectangles.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
When you learn about definite intergals you will have a good idea about what they actually mean.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
is it \[\frac{ ba }{ n } \sum_{i = 1}^{n} f(x) \] ??
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
No wait, that's right.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So yeah you get the idea. It's the sum of all the rectangles multiples by the change in x,(i.e the width) .
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
that's what i did but i got 28 and the answer's 26
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Then you have to use diffrent kinds of rectangles because your answer is correct.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But if you use left rectangles then it's 28.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
why? sorry can u explain?
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
so right hand it's 26 or..?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So this is a very stupid question because it dosen't specify the type of rectangles.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Well right hand is 76 actually.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But it dosen't specify what type of rectangle. Left, right or midpoint.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
where'd the 26 come from? midpoint?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But shall I explain left and right rectangles?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
If you use left, you get 28. If you use right you get 76.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
wait so where did the 26 come from. please explain. i'm so lost. :(
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
26 isn't the correct answer.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
cuz 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...
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Yeah, 28 should be correct. I disagree with the answer.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
If you use 3 subintervals you CANNOT get 26 in anyway.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
The formula would be (2)(f(0)+f(2)+f(4))
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
yeah i did that... and got 28
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Which is absolutely correct.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
It CANNOT be 26 if you use left rectangles.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
if you use right rectangles it's (2)(f(2)+f(4)+f(6)) which is 76.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
yeah i got 28 and 76 but i chose 28. so my teacher is wrong. hmph.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Yep, you teacher is wrong.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
thanks for clarifying. :)
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
In reality the exact value of that integral is 48 but you will learn that later.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
yeah i know. i calculated it.
 one year ago

yun2thejaeBest ResponseYou've already chosen the best response.1
Good 'ol Riemann's screwing with everybody's head.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I just hope I don't have to do it after my first year in uni :/ . AP calc helped so much though XD .
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
ohhhhhhh i think i got it they used average value
 one year ago

oldrin.batakuBest 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)
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
^ Reason why they they should specify the question.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
my friend just assumed that inscribed meant left end points
 one year ago

Dido525Best 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.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
@jennychan12 : That's a flase assumption.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
@oldrin.bataku : If you use midpoints, it's 46 not 26.
 one year ago

yun2thejaeBest ResponseYou've already chosen the best response.1
Lol 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.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I 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 ^_^ .
 one year ago

oldrin.batakuBest 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.
 one year ago

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

Dido525Best ResponseYou've already chosen the best response.1
That's why we have the trapozoidal rule ;) . Ans simpsons rule :P .
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But yes @oldrin.bataku is correct. If they MUST be inscribed then you MUSt use left rectangles.
 one year ago

oldrin.batakuBest 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.
 one year ago

yun2thejaeBest ResponseYou've already chosen the best response.1
Conversation is too much for this PoSci major xD.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I looked at Rungekutta but it makes no sense XD . I am going much deeper into math next year so hopefully then :) .
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Sorry that we turned this page into a discussion @jennychan12 .
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
Nobody drew a damn diagram :P
 one year ago

yun2thejaeBest ResponseYou've already chosen the best response.1
Diagram was drawn in the other thread.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
if u wanna see http://openstudy.com/study#/updates/50d15940e4b069abbb70d3c0
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
that's the same thread as this one...
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
dw:1355899651047:dw That would be incorrect since it does not enclose the curve.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
yeah i got really confused and tried to do another one to resolve my confusion... :D cuz that other person made me confused
 one year ago

oldrin.batakuBest ResponseYou've already chosen the best response.1
dw:1355899646424:dw
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
If you use midpoints it still dosen't enclose the curve fully.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
Inscribed rectangles *should* mean rectangles within the curve, but it sounds like that didn't work, so the damn question is broken.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
It's is 28 though without a doubt.
 one year ago

oldrin.batakuBest ResponseYou've already chosen the best response.1
More than likely your teacher made an error.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
inscribed rectangles would give 26, but i feel like that was already covered in this mess somewhere
 one year ago

yun2thejaeBest ResponseYou've already chosen the best response.1
You haven't done "work" problems in your calc class yet have you?
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
Wait, why isnt the answer 26? 3 inscribed rectangles = area of 26.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
what do u mean? kinetic energy? i do that in physics....
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
@agent0smith can u explain???
 one year ago

yun2thejaeBest ResponseYou've already chosen the best response.1
there are "work" problems you use calculus for. Pray that you do not have to do them xD
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
If you use 3 inscribed rectangles it's 28 not 26.
 one year ago

yun2thejaeBest ResponseYou've already chosen the best response.1
The previous thread came up with 26. this one says 28. let's meet half way and say it's 27...oh wait.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
The 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
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
How'd you get 28, @Dido525
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
left endpoint is 28
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
=(2) * ( f(0) + f(2) + f(4) ) = (2) * ( 2 + 2 + 10 ) = 28
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
Inscribed 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.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
That is not an inscribed rectangle.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
that'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?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But f(0) is inscribed.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
I'll draw it jenny. One sec.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I want to see this too.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
dido, 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.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Isn't that the same thing as inscribed?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Inscribed meaning within.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
No, inscribed means it falls completely within the curve, no jutting out over it.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
okay. i understand that f(1) = 1 but.... oh wait. i see where you're going with this....
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But rectangles will never cover a curve fully, it's impossible.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Like, it covers it fully but it's an overestimate.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
Those are inscribed rectangles, they underestimate the area greatly of course.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Ahh, NOW this makes sense.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But if it's an underestimate, it's not inscribed is it?
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
ok yeah i see it too.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
I googled inscribed rectangles just to be sure.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Wait, why did you do a midpoint for the first rectangle?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Instead of a left one?
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
Because that's the only way to have it inscribed. http://en.wikipedia.org/wiki/Inscribed_figure
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
NOW this all makes sense :D .
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
Inscribed rectangles can be either left or right endpoint
 one year ago

agent0smithBest 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)
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I would give you my medal if I could :P .
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
haha :) this whole confusion was all over the meaning of the word inscribed :D
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Agreed! :D . But hey, this might be n my final so it was good for me too :) .
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
haha 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
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
@jada1701877 : You should have given that to agent.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
thanks so much! and yeah, i went off at like 11 cuz i went to sleep. :)
 one year ago
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