40) The Fundamental Theorem of Calculus Explained

[sukinorules]

THANK YOU SO MUCH. I'm going into highschool in about a week, and this really helped. 

[dameowmixman]

wat .________.

[oHeyitsthatguy]

you're shit hahaha.

[theboombody]

Aw man, you didn't show the clever arithmetic showing how you get from the sigma notation to the definition of the derivative. That's okay though. I can kind of understand why. Youtube isn't really made for such in depth explanation. Actually I think you're more likely to find the proof in real analysis books than calculus books.

[BauraKale]

Here's the Fundamental Theorem of Calculus: "The rate at which area is covered with paint by a paint roller is proportional to the width of the paint roller."

[themanisheab180237ce]

terrible

[frostwow]

hey

this was great

plain and simple

thank you very much

[GR1o6180339887498948]

You should also show how to find the area inside a polar curve or under a surface, that would be exiting.

[TowerCraft]

wheres the proof

[Lutemann]

The proof is found in any calculus book on the market. No reaon to put it up here.

[lateralus011]

I understand how to apply the fundamental theory of calculus however, I don't understand why. Why is the anti-derivative of a line the definite integral? I do not understand why plugging a value into the anti-derivative of a function will give you the area below the curve of the function between zero and that x value. Sigma notation, limits, rectangles, that whole deal makes perfect sense but the jump from the limit to an anti-derivative I do not understand how.

[rls0263]

Yeah, I have the exact same question! I'm taking Calc 3 this spring, and I'm still trying to figure out exactly why the anti derivative of a function would give you the definite integral. I see it's been awhile since you posted this response, have you found an answer?

[b0bb0bs0n]

it just makes so much sense!

[The4thbassguy]

great video!

if you don't mind me asking, what program did you use to create this video??

[Lutemann]

Camtasia Studio

[pssycrssy]

would you make some cal2 videos? if you were teaching it i, and many other students i have spoken with, would definitely take your class

[ryeguy24]

you should prove the fundamental theorem of calculus in a subsequent video.

[Lutemann]

That's done in all the calculus books. What I'm trying to do with these videos is to explain how things work in the simplist terms.

[ryeguy24]

oh ok, i just got excited when seeing the title. Would be a good to see proof visually? in case you having nothing to do this weekend :)

Good video though.

[Lutemann]

Yes.

[4Teddybears]

I have a problem. I think I have worked it out but I would like confirmation. Any help would be greatly apreciated.

I have a function y = 220*e^(-3333.33*x)

I believe that the indefinite integral(anti-derivative) is -.066*e^(-3333.33*x)

This being so, the definite integral of the interval 0 to .0015 (this is an area I want to find) would be:

-.066*e^(-3333.33*.0015)

- (-.066*e^(-3333.33*0))

or .0004447 - (-.066)

which equals .06555(The area under the curve)

Thanks for any help

[4Teddybears]

In addition to the above, I would also like to know whether dividing the area by the interval gives the average of all values of y over that interval.

i.e. .06555/.0015 = 43.7. Is 43.7 the average value of y from x=0 to x=.0015?

[iceman0869]

amazing description... you should be a professor or something :p haha

[onewayx12]

nice ;)

[oxyking]

:) Awesome video's. Really helpful. Night before exam doing a bit of reviewing.. but you do them in 5 min each XD