Calculus - The Fundamental Theorem, Part 1

[Kaiyazu]

I LOVED THIS VIDEO!!! Except the Anti-derivative sign is a capital F in the books..idk why haha

[derekowens]

@Kaiyazu Yes, the capital F notation is fairly common, and I see that used some on AP exams also. The concept, though, is what is critical, and the goal is for it to make sense, in either notation. Glad you liked the video!

DO

[balochan1]

@derekowens, surely you are the bestest tutor that I have seen so far. The way you explain makes maths soo easy. If you were my primary school teacher and taught me this at the age of 7, I am sure I would of passed Calculus course even then, But I have to say I owe you for your time and doing this for students. Thanks a lot, ur truely a LIFESAVER!

[Byron10301]

Derek, can you please tell me what software you are using? I really appreciate it - your handwriting is something out of this world btw. I love the selection of colours as well. I use smooth draw myself, but i find it lacking in many respects.

[elizze6]

But why is the change in velocity the area under the acceleration function? This doesn't make any sense!!

[snowboarder9901]

derekowens for president

[MsBabyBlue0]

There are no words to explain how much I liked this video. Thank you SOO much.

But I have a question. In the second example, we are asked to find the velocity at t=7 sec. So why do we need to find the area under the curve (or the change)? I think we can directly find g(7).

[derekowens]

@MsBabyBlue0 The area under the acceleration curve is what gives us the change in velocity, and we find this area by finding the antiderivative and evaluating, which is what I think you mean by finding g(7). If it starts with a velocity of 0, then the change in velocity from t=0 to t=7 will be the velocity at t=7. Hope that helps, DO.

[xROFLawsonx]

Wow, these are amazing. I love your quick, clear, and clean drawings. what do you use? Very easy to understand.

[mzellars822]

Awesome video. You need to work on those allergies though!

[mariomaruf]

I always thought Khanacademy was good while although slow, but this is so much better, more professional, and both neat and concise. I know I'm subscribing.

[Mrmeanjean]

thank you sir,

[BYMYSYD]

wow, you did a better job than kahn academy. very clear and quick

[leoncio91]

the part 1 is misleading, this is the Fundamental Theorem of Caluculus part 2.

[cheersfornads]

You make Calculus sound great. Thanks.

[TheGlenn9]

can someone tell me where he got his anitderivative value of xcubed from , i get the rest of it but cant figure that bit out ??

[bitty88]

@TheGlenn9 (x^n+1)/n+1

[uitlegklas]

Great! Thanks very much!

[illmatic33]

:-)

[jamescboyd]

Of all the Calculus videos I've seen on Youtube, yours are definitely my favorite. Concise, clear, conceptual - they're really good for understanding the concepts. I'm going to school for engineering and plan on viewing your Physics videos soon! Right now, I'm hoping to survive Calc. 2 online over the summer... Thanks!

[bebancos]

Thanks man,, Great Teaching

[derekowens]

You are correct, there certainly should be a constant! However, when we are calculating a _definite_ integral, the constant disappears. It disappears because it would show up once in g(b) and again in g(a), and we subtract.

I'm going to redo these videos soon, and I'll address the constant of integration when I do.

[xxpettheemokidxx]

just this comment was helpful even. no one ever bothered to clarify what happened to adding a constant during the area problems when using integrals.

[CigarStudLasVegas]

should the antiderivative not have a constant factor added for the general form of the antiderivative,

[ayezeee123]

thank you

[derekowens]

These "Fundamental Theorem" videos are about to get redone. I think I can improve the explanation.