Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

Category:

Education

Tags:

• Calculus
• Fundamental Theorem
• Integral
• Integrating
• Integrate
• homeschool
• homeschool math
• Derek Owens
• distance learning

[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

[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.

[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.

[derekowens]

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

[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

[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!