RIEMANN SUM to find estimate of distance travelled

[latent spire]

My actual travel distance was 3.44 miles, and I am trying to use riemanns square to estimate my travel distance. All of my estimates (RRAM, LRAM, etc) are overestimates. Are they correct? I need help

[wise sierra]

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[icy wadi]

Good lord

[grave harness]

I'd just do it in Excel...

[latent spire]

But it’s on paper, it’s paper project

[grave harness]

Quite a hassle to do all that by hand.

[latent spire]

what

[grave harness]

Surely they don't expect you to write the full sums of dozens of terms.

[latent spire]

We can use a calculator but we have to write the work we do on paper

[icy wadi]

That's a lot of stuff written down

Also it looks kinda unreadable

[latent spire]

😡

[icy wadi]

Like where is your right riemann sum?

[latent spire]

Use sharingan

Top of last picture

[icy wadi]

Dude cmon

[latent spire]

411minutes*MPH or 6.8 miles^2 when converted

[grave harness]

Don't be rude.
At least you can check it in Excel.

[icy wadi]

I am so deadass right now but I cannot see where it is

[icy wadi]

no, like your actual representation on the graph pictures

[icy wadi]

I see a left riemann

[latent spire]

oh

OHHH

[icy wadi]

But it's like mixed with the right riemann

So I can't tell if you accurately derived it or not

Ykwim

[latent spire]

yea just take away the leftmost value and there’s the RRAM

that’s what I did I just ignored the leftmost rectangle

And dude base times height times the 1, because there is a change of 1 unit for every minute

Did that answer ur question

I used same graph for RRAM, LRAM, MRAM

and trapezoids

Because lazy

[icy wadi]

Okay

I'm studying rn

Give me a second

[latent spire]

R u still studying

[icy wadi]

Not now

[icy wadi]

Yeah, I’ll try to look further now

[latent spire]

How did looking further do

My teacher said it’s basically very unlikely that I overestimated every estimate

.

[dense dust]

Nah vro 💀💀💀

[latent spire]

PLZ VRO PL

Plz

[dense dust]

No one’s checking that 💀

[latent spire]

Think abt it bro we will both benefit from this bro

[dense dust]

Way too much work

[latent spire]

Our brains will be HUGE

bro pl

Plz

[dense dust]

No, not really

[flat beacon]

I have a question.

[dense dust]

Make a new help post

[latent spire]

Yes

[flat beacon]

It’s literally one question. Nothin major. What’s 24 divided by 2?

[latent spire]

Torrent save me

[dense dust]

Check your answers with a calculator

[dense dust]

12

[flat beacon]

Thanks

[latent spire]

I did - I used scientific calculator and Desmond

Desmos

[dense dust]

And did your answers check out?

[latent spire]

Is there another calculator I should use?

They are all overestimates

Which apparently never really happens

[dense dust]

Can you put the data into excel at least

[dense dust]

Yeah it wouldn’t make sense

[latent spire]

:(this is hard vro

What will excel do

[dense dust]

Make it look neat so that I’m actually motivated to help you

[latent spire]

Which part needs to look neat

[dense dust]

The table of values

[latent spire]

OOOOOOO

[dense dust]

I’m not reading all that

[latent spire]

wait what

Is it that bad

Are the numbers not legible

[dense dust]

Organize it and I’ll read it

[dense dust]

No, it’s just too much math

[latent spire]

Oh ok

BRB

[latent spire]

Look

Can u help now plz

[flat beacon]

@latent spire

Let’s go with trend analysis and see if we can identify a pattern!

Since your scatter plots show data clustering between 20-30 on the vertical axis, we can ask: Is there a clear direction in how the data moves?

1. Visual Check: If most points align horizontally, the data might represent stable values over time. If they incline, it could show growth. A decline? That suggests a decrease.
2. Possible Correlation: Are the points forming a recognizable shape like a linear trend or curve? If so, I could suggest fitting a function to describe it mathematically.
3. Outliers & Variability: Any data points that sit way outside the cluster might represent unique events or errors.

If you want a deeper breakdown, I could explore a best-fit line or another mathematical approach. What do you think?

[latent spire]

This was the result of transportation speed during each minute (until 15 minutes is reached). I just want to know if my mile estimations were correct

[humble moon]

Bro is this greek 💀

[latent spire]

No bro plz

[latent spire]

U know calculus PLZ HELP

I will show u a picture of my 3 year old cat if u help

[humble moon]

i would love to help except I CANT READ WHATS WRITTEN !!

[latent spire]

I WILL REWRITE WHAT CANT U READ

[humble moon]

U just summed the datas not the areas 💔

[latent spire]

FUCKKKKKKK

what do I do bro

I converted the estimates into miles

Is that not area?

[latent spire]

?

[humble moon]

noooo

oh wait

yee it is the area

[latent spire]

WAIT

[humble moon]

but i dont see you converting them to miles 🔥

maybe im reading it wrong

[latent spire]

ILY SM

o

It’s the last page

Hold on

[humble moon]

,rotate

ayo

[latent spire]

Changed the MPH*minutes to miles to get area

[icy wadi]

I’m studying now, I went for a run

[icy wadi]

Oh hey, it’s ravi

And wolf

I’m sure they’re both capable enough to cover this

[latent spire]

Ravi abandoned ship faster than my dad VRO

It’s Alr tho

[flat beacon]

Let f(x) be a function such that \int_{-\infty}^{\infty} f(x) , dx converges to the number of socks missing from your laundry. Given that the divergence of the gradient of the curl of f(x) is equal to the number of times you've lost your keys this week, prove that the limit of e^{i\pi} + 1 as x \to \text{your last brain cell} is equal to a pizza with infinite toppings

[latent spire]

Wolf id trying

[icy wadi]

Shut this GPT ahh response up

[flat beacon]

It was copilot.

Not gpt.

[icy wadi]

It’s AI bro

[flat beacon]

No it’s not.

[icy wadi]

Anyways if you can’t actually help then respectfully get out

[flat beacon]

Copilot. Is Artificial intelligence.

[latent spire]

Get away

[flat beacon]

Not AI.

[icy wadi]

^

[flat beacon]

im trying to help

You won’t let me

[icy wadi]

Sure buddy...

[flat beacon]

ok ask me a question

[icy wadi]

?!

[latent spire]

Can u help plz

[icy wadi]

Dude just get out seriously

[latent spire]

I just need to find area and convert to miles

[icy wadi]

I’m trying to get this brain dead monkey out

[flat beacon]

Bro. Im trying to help him out

[icy wadi]

I’ll try to find the values

[latent spire]

I already did I just need to check my answer

Thx bro

[latent spire]

I’m a woman

[flat beacon]

oh shit

[latent spire]

Why does everyone think I’m a man

[flat beacon]

My bad

[icy wadi]

I can tell you’re not, so I’m going to just timeout you

[humble moon]

Arent u only supposed to calculate the low3r and upper 💔 , plus the lower is def lower what are u yappering about

[icy wadi]

Hopefully that’ll shut you up and make you realize trolling in help threads is not allowed

[latent spire]

I’m supposed to calculate the LRAM,MRAM,RRAM, and trapezoid thing

Then convert to miles

[icy wadi]

-timeout @flat beacon 10m Trolling/using AI in help threads, do it again and it’ll last longer

[sick idol]

⏱ Timed out _boogiewoogie__ for 10 minutes

[icy wadi]

Lemme get on my PC

[latent spire]

I could hug u rn thx bro

[icy wadi]

I’m sorry dude, I’m trying to finish up my mock exam 😭but I’ll let wolf handle it

If his smartass cant I’ll see if I can try again

[latent spire]

Ok

[humble moon]

I genuinely don't know what MRAM and TRAM are, so i'm sorry i can't lol

i only know upper and lower !!

[latent spire]

Middle estimate and trapezoid estimate

[dense dust]

Wait how tf are you able to get overestimates and underestimates

Do you have an explicit function that describes whatever you’re trying to integrate??

[latent spire]

Like-

[latent spire]

The function is the graph

[dense dust]

Nah I saw it, you have the actual distance travelled

3.44 miles, right?

[latent spire]

I know they’re overestimates because they are higher than my actual travel distance if 3.44 miles when converted

Yes

[dense dust]

Alr, let me cook

[latent spire]

COOK PLZ

[dense dust]

,calc (30+31+39+40+26+16+20+39+18+18+19+29+22+25+27)/60

[nimble bear]

Result:

6.65

[dense dust]

Wtf??

[latent spire]

What

That’s what I got

[dense dust]

LRM

Right?

[latent spire]

6.65 miles for LRAM

yeah

[dense dust]

Ok, RRM now

[latent spire]

Why did u say WTF tho

YESSS KEEP COOKING

[dense dust]

,calc (31+39+40+26+16+20+39+18+18+19+29+22+25+42+27)/60

[nimble bear]

Result:

6.85

[dense dust]

I was surprised

[latent spire]

For RRAM?

[dense dust]

Yeah

6.85

[latent spire]

YES I GOT THE SAME

keep cooking my savior, the stove is hot

[dense dust]

Ok - I’m at school now, but I’ll calculate the others soon

5 minutes

[latent spire]

OK!

Thx

[dense dust]

Ok, MRAM

I’ll need desmos to type this one out

[latent spire]

Ok

U r life savior

🫂

[grave harness]

I mean, I'd still do it in Excel.

[dense dust]

Is the MRAM 6.6?

[latent spire]

O

I got 4

Isn’t MRAM like every other point?

[dense dust]

No?

[latent spire]

Oh

How did u find that

[dense dust]

You take the average of the left and right points

Which is also the exact same as a trapezoidal Σ 💀

Whatt

,w Midpoint Riemann Σ

[nimble bear]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by inverse_cupid

[latent spire]

Omg wtf American education is fucking me up

[dense dust]

,w Midpoint Riemann Sum definition

[nimble bear]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by inverse_cupid

[latent spire]

MMRAM is the same as trapezoidal?

[dense dust]

Well the way it was defined to me it looks like it 💀💀💀

[latent spire]

How? Do I divide by two? I’m deadass not understanding

[dense dust]

Add and divide by 2

[grave harness]

No.
Trapezoidal uses (f(a) + f(b))/2, midpoint rectangular uses f((a + b)/2). A bit different.

[dense dust]

Yeah I figured 😭

@latent spire your method’s correct

[latent spire]

WAIT

did I get the right answer

Or is ur answer still right

[grave harness]

The result will be especially apparently different if the function is convex in the same direction over the whole region of integration (since Jensen's inequality can be applied for every point).

[dense dust]

I don’t get how the MMRAM can be applied here 💀

[latent spire]

What I did was

[dense dust]

That inequality gives me trauma

[grave harness]

Oh, if all you have is points and you only use linear interpolation, then trapezoidal and midpoint rectangles give the same thing, as in that case (f(a) + f(b))/2 = f((a + b)/2).

[dense dust]

Yeah

We don’t have an explicit function here

[latent spire]

I draw line between three points and the middle point got added to the MRAM

then you take all the MRAM points and multiply it by the height of 1

[dense dust]

42 is an endpoint

Honestly

I have a hypothesis about what this car is behaving like

[latent spire]

Yeah 42 is an endpoint

[latent spire]

It was bus drive to school

[dense dust]

So you can’t use it for MMRAM

[dense dust]

That makes sense

[latent spire]

OH WAIT REALLY

thx bro

[dense dust]

But then you have to account for the last rectangle somehow

[latent spire]

oh

[grave harness]

I assume the first table is the data you've been given?

If so, I can try calculating the sums, too.

[latent spire]

Yea

[dense dust]

Personally, this thing’s speed is probably stitched up by a bunch of concave up functions

[grave harness]

Alright. I'm going to be busy in several minutes, so please remind me in a couple of hours.

[latent spire]

Can MRAM point not be an end point?

[dense dust]

Nope

[latent spire]

Okok

[latent spire]

Ig the only other choice is to ignore it?

[dense dust]

Then the approximation will be off

I think trapezoidal and midpoint will be the same tbh

[latent spire]

OH WAIT

[dense dust]

Linear interpolation

[latent spire]

U MAY HAVE COOKED

Because when I removed the 42

My new total distance when converted to miles is

3.3

Which is very close to the actual distance

And isn’t MRAM the most accurate estimate

[latent spire]

Opinion?

Also CHATGPT agrees with you on the endpoint thing

Yeah I got 6.6 on trapezoidal, which u got for MRAM, but I got 3.3 (after recalculating now) for the MRAM

[grave harness]

Here's what I got.

[latent spire]

Is the trapezoidal and MRAM the same?

[grave harness]

Yes.

[latent spire]

I got 6.6 miles for trapezoidal

[grave harness]

For this reason.

[latent spire]

How did you get 6.75

[grave harness]

Trapezoidal is always equal to the arithmetic mean of left and right rectangles, so no.

[latent spire]

Oh

[latent spire]

How did you get that? Divide by two after adding LRAM and RRAM?

Then divide by 60?

[grave harness]

Well, those are already divided by 60 min/h. Other than that, yes.

[latent spire]

Oh

That makes sense

I wonder why my teacher didn’t mention MRAM and trapezoidal are the same

[grave harness]

Not in general.

They are only the same when you only have data as points (as opposed to an equation) and when you linearly interpolate the points to get the midvalues.

If you have an equation or you use, for example, quadratic interpolation, then they won't be the same.

[latent spire]

Also I wish we learned this faster way, my teacher said to do base1 +base2/2 for every trapezoid

[latent spire]

Ok

[grave harness]

Well, yeah. We have (for equal intervals):
S(LR) = hΣ(f(x(i - 1)), i = 1 to n)
S(RR) = hΣ(f(x(i)), i = 1 to n)
S(T) = hΣ((f(x(i - 1)) + f(x(i)))/2, i = 1 to n)
From here it's pretty obvious that S(T) = (S(LR) + S(RR))/2.

As for MR:
S(MR) = hΣ(f((x(i - 1) + x(i))/2), i = 1 to n)
So, for T and MR to be the same, we need (f(x(i - 1)) + f(x(i)))/2 = f((x(i - 1) + x(i))/2), which works for linear functions.

[latent spire]

OH I SEE WHY WE HAVE DIFFERENT ANSWER

[latent spire]

My lord

At 7 it’s 30 not 39

My handwriting is ass sometimes

lol

Sorry

[grave harness]

Oh. One sec.

Here you go.

[latent spire]

THANK YOU

WE HAVE THE SAME ANSWERS

[latent spire]

Bro ur amazing

Thx

[grave harness]

You're welcome!

I hope you'll heed my advice on such calculations in the future 😄

[latent spire]

Long live LordDarpinger

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@latent spire

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