With a combination of khan academy and your videos on the fundamental theorem of calculus I now have an intuitive understanding of what calculus is and what it is used for. Only took 1.5 years of searching for someone who could explain it properly and in an intuitive way.
I think that you have a valid point. Not the most intuitive choice of words. Newton actually called them "fluxions", which is a term that seems to make more sense to me than "derivatives".
Im having trouble understanding a definite integral that starts from 0 to x where at A(0) there is a area. For example, the integral of the square root of (1+x^2) multiplied by x^5, Where the antiderivative at A(0) is a positive number that is 0.0769. whats the reasoning of this? shouldn't the area of 0 just be 0? what also confuses me is that the graph of the function at point 0 is 0, but the area at that point is 0.0769.
In every video I see where the basic concept of calculus is attempted to be introduced, there is the sudden introduction of the antiderivative being X cubed / 3. Where does that come from?
x^3/3 is the anti-derivative of the function x^2. The function y=x^2 is often used when introducing the concept of integration, because it is a function that students are typically familiar with, and because it is a relatively simply non-linear function. The anti-derivative of y=x^2 is y=x^3/3, so that particular anti-derivative ends up showing up a lot in calculus courses.
You said "A(x) changes quickly because the height of the function is large," which is false. The height doesn't affect the rate of change of area. It's the rate of change of the height that affects the rate of change of the area. Increasing slope = More area change for every small change in x Decreasing slope = Less area change for every small change in x
You're not correct. .Area is always increasing as X increases, even when slope is flat. At minimum Y values, whether the slope is steep or flat, the area is only changing by small amounts. This is because area is X times Y. Even if Y is constant, if its value is great, the change in area is great as X increases. By what you said, no slope = no change in area. Not true. Think of it in terms of numerical values. If Y is 10 and delta X is 1 them area is 10. If Y is 10 and delta X is 2, then area is 20. An increase of only 1 on the X axis doubled the area. Whereas if Y is 3 and X goes from 1 to 2, the area only increases by a little. Has nothing to do with slope.
When you see "dx" just think "Delta x". It's a change in x, or an interval on the x-axis. The key idea, though, is that dx is really really tiny, basically infinitely small, while Delta x is typically in interval of some measurable size. dx is so small that it is essentially zero in some contexts. (3 + dx is equal to 3, for example). dx, being infinitely small, is what we call an "infinitesimal" quantity. f(x) is the y value, or height of the function. dx is a tiny horizontal increment, or a tiny width. f(x) times dx is a tiny little vertical strip of area on the graph. It is this area that is important here. We multiply the height times the width, f(x) times dx, to get the area. We're dealing with an infinite number of infinitely small areas. This is a great topic for an Infinite Being to consider.
Not necessarily. Here are my thoughts off the top of my head: calculus and physics definitely overlap, and Newton invented both, and he essentially invented them together. He developed calculus to solve certain problems in physics, at least in part. In a calculus course, some physics concepts are also typically covered, such as the equations of motion. And in calculus, students will often see some homework problems that are essentially physics problems. Having had high school physics prior to college calculus might not be strictly required but could be very helpful. A more complete understanding of physics requires calculus. But a lot of the fundamental physics concepts can be understood using only basic algebra. High school level physics is typically algebra based, while college level physics is typically calculus based. Hope that helps!
With a combination of khan academy and your videos on the fundamental theorem of calculus I now have an intuitive understanding of what calculus is and what it is used for. Only took 1.5 years of searching for someone who could explain it properly and in an intuitive way.
Curious Kid, my thoughts exactly! These are the best calculus videos on RUclips. Derek Owens is to calculus what Gutenberg was to literacy.
Thanks very much Derek Owens. You are Good, excellent, Superb,outstanding, exceptional, marvelous, wonderful, magnificent. You are blessed.
Mr. Derek Owens, you are a genius of explaining
THE PERSON WHO INTRODUCED THE WORD DERIVATE AND INTEGRAL MADE ALL THE CONFUSION .. MANY SUFFERING TO UNDERSTAND THIS STUFF .
I think that you have a valid point. Not the most intuitive choice of words. Newton actually called them "fluxions", which is a term that seems to make more sense to me than "derivatives".
Thank u Mr. Derek. I'm a Student from Indonesian High school can solve some basic calculation of calculus now! it's very useful! once again, thank u !
Derek Owens should be given a medal of the best teacher in the world!
Best RUclips channel to me 💖💖💖💖
Am a student from universtiy of goroka (PNG) .Thankyou for video really helping me with calcalus
Your tutorials are gold.
You are such a good instructor!!!
The "Part 2" in the title of this video just indicates that it is the second video in the series. Sorry for the confusion.
Im having trouble understanding a definite integral that starts from 0 to x where at A(0) there is a area. For example, the integral of the square root of (1+x^2) multiplied by x^5, Where the antiderivative at A(0) is a positive number that is 0.0769. whats the reasoning of this? shouldn't the area of 0 just be 0?
what also confuses me is that the graph of the function at point 0 is 0, but the area at that point is 0.0769.
Best explanation for Fundamental theorem of Calculus I've ever heard. Great work, keep up.
Dude, you are the best. Thank you.
Excellent presentation.
good lessons for everyone who needs to learn maths
Well Explained. Thanks.
Well explained 👌
Hi! Could you share with us what it is the name of the application you are using?
thanks a lot.
In every video I see where the basic concept of calculus is attempted to be introduced, there is the sudden introduction of the antiderivative being X cubed / 3. Where does that come from?
x^3/3 is the anti-derivative of the function x^2. The function y=x^2 is often used when introducing the concept of integration, because it is a function that students are typically familiar with, and because it is a relatively simply non-linear function. The anti-derivative of y=x^2 is y=x^3/3, so that particular anti-derivative ends up showing up a lot in calculus courses.
You said "A(x) changes quickly because the height of the function is large," which is false. The height doesn't affect the rate of change of area. It's the rate of change of the height that affects the rate of change of the area.
Increasing slope = More area change for every small change in x
Decreasing slope = Less area change for every small change in x
You're not correct. .Area is always increasing as X
increases, even when slope is flat. At minimum Y values, whether the
slope is steep or flat, the area is only changing by small amounts. This
is because area is X times Y. Even if Y is constant, if its value is
great, the change in area is great as X increases. By what you said, no slope = no change in area. Not true. Think of it in terms of numerical values. If Y is 10 and delta X is 1 them area is 10. If Y is 10 and delta X is 2, then area is 20. An increase of only 1 on the X axis doubled the area. Whereas if Y is 3 and X goes from 1 to 2, the area only increases by a little. Has nothing to do with slope.
thank you. your videos are really helpful.
Great stuff!!!
If the graph is moving up then down
Split it into two parts a to c and c to b
g (c) - g (a) + g(c) - g(b)
very simple approach
Thank you. Love it.
what's the dx in the integral f(x) dx? the function f(x) makes sense, but why add dx?
When you see "dx" just think "Delta x". It's a change in x, or an interval on the x-axis. The key idea, though, is that dx is really really tiny, basically infinitely small, while Delta x is typically in interval of some measurable size. dx is so small that it is essentially zero in some contexts. (3 + dx is equal to 3, for example). dx, being infinitely small, is what we call an "infinitesimal" quantity.
f(x) is the y value, or height of the function. dx is a tiny horizontal increment, or a tiny width. f(x) times dx is a tiny little vertical strip of area on the graph. It is this area that is important here. We multiply the height times the width, f(x) times dx, to get the area.
We're dealing with an infinite number of infinitely small areas. This is a great topic for an Infinite Being to consider.
@@derekowens thank you very much for the clear explanation. I can only wish you were around in 1969 to teach calculus.
what software do you use to make your videos?
rcfoley 9gag
5:45 isn't it supposed to be the other way round?
Should the study of physics come before study of calculus ?
Not necessarily. Here are my thoughts off the top of my head: calculus and physics definitely overlap, and Newton invented both, and he essentially invented them together. He developed calculus to solve certain problems in physics, at least in part.
In a calculus course, some physics concepts are also typically covered, such as the equations of motion. And in calculus, students will often see some homework problems that are essentially physics problems. Having had high school physics prior to college calculus might not be strictly required but could be very helpful.
A more complete understanding of physics requires calculus. But a lot of the fundamental physics concepts can be understood using only basic algebra. High school level physics is typically algebra based, while college level physics is typically calculus based.
Hope that helps!
Derek Owens it does. Thanks for reply
Well done!
You have such pretty handwriting.
Yep.
Good stuff!
I has nit seen this explained this way before
Thanks
awesome! :)
Understand the fundamental theorem of calculus in 3:52 min
watch?v=nwDkRItiBAs
this is weird. in my book this is FTC 1