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O_o .

sorry typed something wrong. and that 1 is supposed to be an A

so
i got the integrated area to be 48, so answers either a b or c

Wait.

Wait, what kind of rectangles? Left, right, or midpoint?

the problem doesnt say. i'm assuming left

cuz it says inscribed

Well you are right. It's either A, B or C :D . Now can you do it out? :) .

\[\Delta(x)=\frac{ 6-0 }{ 3 }\]

i'm confused
my friend says to use riemann sum.
what's the formula for that?

\[\Delta(x) = 2\]

In this particular example, a Riemann sum is basically the sum of the individual rectangles.

When you learn about definite intergals you will have a good idea about what they actually mean.

is it \[\frac{ b-a }{ n } \sum_{i = 1}^{n} f(x) \] ??

No wait, that's right.

that's what i did but i got 28
and the answer's 26

Then you have to use diffrent kinds of rectangles because your answer is correct.

26 or 28 ?

It's 26.

But if you use left rectangles then it's 28.

why? sorry can u explain?

oh.

so right hand it's 26 or..?

So this is a very stupid question because it dosen't specify the type of rectangles.

Well right hand is 76 actually.

But it dosen't specify what type of rectangle. Left, right or midpoint.

where'd the 26 come from? midpoint?

No, midpoint is 46.

But shall I explain left and right rectangles?

If you use left, you get 28. If you use right you get 76.

Shall I explain?

wait so where did the 26 come from.
please explain. i'm so lost. :(

26 isn't the correct answer.

oh.

Wait hold on.

Yeah, 28 should be correct. I disagree with the answer.

If you use 3 subintervals you CANNOT get 26 in anyway.

The formula would be (2)(f(0)+f(2)+f(4))

yeah i did that...
and got 28

Which is absolutely correct.

It CANNOT be 26 if you use left rectangles.

if you use right rectangles it's (2)(f(2)+f(4)+f(6)) which is 76.

yeah i got 28 and 76 but i chose 28.
so my teacher is wrong. hmph.

Yep, you teacher is wrong.

thanks for clarifying. :)

In reality the exact value of that integral is 48 but you will learn that later.

yeah i know. i calculated it.

Kk.

Good 'ol Riemann's screwing with everybody's head.

I just hope I don't have to do it after my first year in uni :/ . AP calc helped so much though XD .

ohhhhhhh i think i got it
they used average value

LOL

^ Reason why they they should specify the question.

my friend just assumed that inscribed meant left end points

@jennychan12 : That's a flase assumption.

false*

That's why we have the trapozoidal rule ;) . Ans simpsons rule :P .

and*

MUST*

Conversation is too much for this PoSci major xD.

Sorry that we turned this page into a discussion @jennychan12 .

it's aiight.

Nobody drew a damn diagram :P

Sigh...

Diagram was drawn in the other thread.

^ haha yes

|dw:1355899568667:dw|

Something like that.

that's the same thread as this one...

LOL

|dw:1355899651047:dw|
That would be incorrect since it does not enclose the curve.

|dw:1355899646424:dw|

|dw:1355899717852:dw|

If you use midpoints it still dosen't enclose the curve fully.

Damn question.

It's is 28 though without a doubt.

More than likely your teacher made an error.

yeah

inscribed rectangles would give 26, but i feel like that was already covered in this mess somewhere

You haven't done "work" problems in your calc class yet have you?

Wait, why isnt the answer 26? 3 inscribed rectangles = area of 26.

what do u mean?
kinetic energy? i do that in physics....

@agent0smith can u explain???

there are "work" problems you use calculus for. Pray that you do not have to do them xD

If you use 3 inscribed rectangles it's 28 not 26.

lol

How'd you get 28, @Dido525

left endpoint is 28

=(2) * ( f(0) + f(2) + f(4) )
= (2) * ( 2 + 2 + 10 )
= 28

That is not an inscribed rectangle.

But f(0) is inscribed.

I'll draw it jenny. One sec.

I want to see this too.

Isn't that the same thing as inscribed?

Inscribed meaning within.

No, inscribed means it falls completely within the curve, no jutting out over it.

okay. i understand that f(1) = 1 but....
oh wait. i see where you're going with this....

|dw:1355900439887:dw|

But rectangles will never cover a curve fully, it's impossible.

Like, it covers it fully but it's an overestimate.

Ohh shoot! O_o .

Those are inscribed rectangles, they underestimate the area greatly of course.

Ahh, NOW this makes sense.

hahah :)

But if it's an underestimate, it's not inscribed is it?

ok yeah i see it too.

I googled inscribed rectangles just to be sure.

Wait, why did you do a midpoint for the first rectangle?

Instead of a left one?

Because that's the only way to have it inscribed.
http://en.wikipedia.org/wiki/Inscribed_figure

NOW this all makes sense :D .

Inscribed rectangles can be either left or right endpoint

or midpoint

@jennychan12 you see how it's 26 now? the height of the first is f(1), next is f(2), then f(4)

I would give you my medal if I could :P .

haha :) this whole confusion was all over the meaning of the word inscribed :D

Agreed! :D . But hey, this might be n my final so it was good for me too :) .

She is offline :/ .

@jada1701877 : You should have given that to agent.

thanks so much! and yeah, i went off at like 11 cuz i went to sleep. :)