The Definite Integral

[robertocontadorpn]

Just an excellent work! people like you is needed! I'm From Argentina! my regards

[iiottoii]

shouldnt it be 0 to 4?

[Gobsnachaz]

@brightstorm2 Is the rectangle method that you used, taking the upper and lower approximate sum, the same as Darboux integrals? Thanks, good video.

[merajahmad1991]

this video was really helpful...thank you!!

[mahanghasemi]

i f*#in <3 U man!!!

[mzgemini0006]

I Love the introduction, however I might have to go on you guys website because I learn much better with examples

Great Video....

[jazzguitar2010]

Can you please tell me what video camera you're using to record these videos? The quality is superb.

[jazzguitar2010]

Very sharp presentation, well done.

[elizze6]

Gahh What I don't understand is why the definite integral is the same thing as area. Why can't I find anything explaining that? Everything just says they are the same, but why does taking the antiderivative of the function at the upper and lower limit and subtracting them get you area?

[plaetarsikcky]

@elizze6 This video does explain that... that's what the whole thing about the rectangles is about, the idea is that if you have an infinite number of rectangles, you have the exact area.

[elizze6]

@plaetarsikcky Yeah, but then why is the definite integral the same thing as the antiderivative?

[illuzion30]

@5:00: But why is the definite integral the same as that summation?

[lillibeth13]

@illuzion30 The integral is a function that is an antiderivative of f...if you were to evaluate it at a and b respectively you'd find the EXACT area under the curve of f(x) from a to b. The summation and the integral are practically equivalent because you're taking the limit as the number of rectangles approaches infinity...if that happens then the width (delta x) gets smaller and smaller until there is NO rectangle and you'd have the exact area.

[illuzion30]

@lillibeth13 That doesn't make it clear to me. I still don't see the connection. You've not really explained why the antiderivative is equal to the summation.

[AlbertaSun]

I suspend judgement as to whether or not 1 is exactly the same as 0.999... (repeated)

Leibniz's law means if two things are exactly the same, then they must share all their properties.

[AlbertaSun]

I have a question. Is 4.9999999999...  exactly the same as five?

[Ntalikeris666]

@AlbertaSun If the nines are infinite, yes. Similar Example:

1/3+1/3+1/3=1

But, 1/3=0,333... So 0,333+0,333+0,333=0,999...

From the two above => 1 = 0.999...

[natlieify]

muit obrigado.......



[Amyga17]

I decided to learn precalc and calc over the summer, because I'm a cool kid like that. I wouldn't have been able to do it without your website's videos and examples, thanks a ton!

[priyakoko]

THNX A LOT!!!!!!!!!!!!!!!!!!! <3 U!!!!!!!!!!!

[mohamed1917]

please come teach my calc class! haha jk, but thanks a ton

[jackliuliu]

might wanna give a few examples next time.

[brightstorm2]

@jackliuliu Hey there, if you go to brightstorm website, there are videos for example problems there. :)

[xXxMidNightRosexXx]

Thank you!



[Mrmeanjean]

Thanks you

[MsKhadijahCamille]

really good explanation. i would highly recommend based on this vid.

[airhendrix47]

poindexter...you rock my calculus socks

[naoufelabs1]

Nice course.