Riemann Sums, Finite Sums, and Integrals Part 1

[VVillowz]

Thanks for the video. But, can you fix the audio?

[SakibiHabibi]

this guy is funny but he makes a terrible teacher. KHAN AND PATRICKJMT FTW!

[Ironkiller22]

I´ve been reading Spivak´s Calculus and i don´t get what does mean U(f,P)-L(f,P) < e, where U(f,P)=upper sum and L(f,P)=lower sum???

[TheVarrBacon]

Thanks a ton! Really helped!

[kdurnfor]

Ok. So this helps a lot! A great video to understanding the basics of integration.

But is anyone else noticing that he has chew in his mouth??

[qstong]

awesome teaching!!

[Pikashaft]

"Takes off like a hockey stick"?

[edwebo]

i think hes alluding to the fact that the hockey stick (grass hockey) if pictured as a circle (more like an oval) then all or most of its mass is biased to one side.

i think lol otherwise hes just talking crap. quite funny crap but still crap.

sweet vid btw

[KalShaen]

@Pikashaft yea. it takes off like a hokey stick because a hokey stick gets a little curve and then just shoots up if ur looking on the inside part of the stick. much like a squared function

[seekluv]

this guy is funny.

[beingbanana]

his mouth is so long :-S

[narutoyondaime14]

thank you so much for the tutorial!

[atakach98]

i agree this is crap

[RobotTed]

Riemann sums are not crap. Reducing Calculus to pure technique is great for most things, but can lead to surprises.

Removing all irrational numbers from the line such as 2^0.5 and then summing all rational numbers that are left leads to a paradox: the area is the same, but we removed many rectangles.

And so, the function f(x) needs to be continuous.

[RobotTed]

(continued)

Division by zero also creates trouble, as you can have and infinitely long, infinitely thin strip in a function.

f(x) = 1/x is such a function. If you try and sum it when it's value is 1/0 you get a logic error.

To sum it, you have to "cut" it in half at the zero, and sum both sides of 1/x separately from [-infinity, 0[ on one side to ]0, infinity] on the other.

And so, the function f(x) can't be divided by zero.

[Fernandez40]

good explanation, it really helped. Thanks a lot.

[desione07]

"forget all this crap" ..lol, exactly.

[juhnae]

This was extremely helpful! Most books and websites were of no assistance to me, but this really made Riemann Sums clear!

[TSmirk]

Will you be posting your educational background on your channel soon?

[azndude444]

wow this really helped me thxs

[alinjohn1960]

smiley man!!!

[DarkNinja141]

damn ur good looking. . .

[ghodium]

you definitely not on the Autistic Spectrum

[ghodium]

good vid, you explain the concepts well

[ghodium]

Riemann "suffered from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as fantastic calculation abilities, from an early age, but suffered from timidity and a fear of speaking in public"... possibly Aspergers syndrome or some autistic Spectrum Condition

[ghodium]

the term Riemann Sum also gives recognition where it is deserved, to the man who gave us this, he "made important contributions to analysis and differential geometry, some of them paving the way for the later development of general relativity"

[supreme0death0bringe]

hahaha ur answer wasnt even close enough to the real one..

[debunker1905]

What's the name of the board markers you use? Please I need them.

[ink942]

thanks

[kuspise]

:P -.-

[kkkkulo]

Hey boy, you are an excellent teacher. Thabk you!

;)

[capoate]

you're from minnesota aye? "it takes off like a hockey stick"

[mimiloloy]

thankss for ur vid!

i watch it b4 the day i took the test

& yay

i got all Riemann sum stuff on the test rite :D

[artanis77z]

You really make my world of high school a better place. Thanks for your vids.

[terminaterjohn]

forget all this crap!!!!!!

[artanis77z]

lol

[isabelmaples]

What if you had a function y=2x^2+1 over the period [1,2] with four intervals. I just don't understand how you originally graph each function

[Jazzwoman1985]

I do not understand what do you mean by left f(x) and right f(x) and why did you square the numbers?

[midnighttutor]

left and right correspond to the two sides of each strip and we are squaring them because that is what the function says to do (x^2)

[bkjoelover]

i like your mouth; you're cute.

[metebayram44]

studying calculus is awesome

[CorruptedSeducer]

whoa. this dude has a huge ass jaw...!!1

[Romi260986]

btw i think you explain very well....keep it up! greetings from Venezuela

[Romi260986]

Riemann summs without infinite limits are useless, its just an aproximate value...integrals are more helpful

[xxxxLAMBOFGODxxxx]

hey thats pretty good! Riemann summ is not bad, but why not just use fundamental theory of calculus? Also, Im just curious if you can show how to do series and sequences, such as test of convergence and all that....That's where I'm having a bit of trouble.

[frlool]

a lot better explained than profesor did tel lus in school :) 5 stars :)

[protheory]

Hi, I've solved the Riemann Hypothesis if you're interested :)

I wrote a theory of everything that solves literally everything, I've also solved all the other Millennium Problems as well.

[midnighttutor]

Ok great....who shot Kennedy?

[protheory]

Thanks for the response. According to my theory he did get shot, didn't get shot plus neutral if that helps :)

[RiemannCalculator]

Please explain your theory! I'm extremely interested.

[carlisiano]

he hasn't solved it, he's just got some nutcase "Positive something vagina" theory he's preaching, which is comparable to scientology.

The hodge conjecture was lol, he starts of the video with "basically.." THE HODGE CONJECTURE IS NOT BASIC

[madjuggla9]

It's not a theory, it's a mathematical proof. If you can't understand it at this level of teachin, your either retarded or lazy.

[carlisiano]

I was talking about protheory's comment you muppet. Unless you were talking to someone else, in which case...carry on.

[48phantom]

Good intro to Riemann sums. Good tie in to integration in part 2.