Nice visualization. :) But you should have included a remark that the integral symbol is simply an elongated S, representing the sum of all the rectangles.
I didn't get it , f(x) of each rectangle is different, so unless we calculate the area of each rectangle seprately . How adding them all will give us area Under curve ?
u should be grateful..u are born in this era ..where such videos are there which could help anyone to understand difficult concept of calculus..back then when we are born ..we didnt have such resources ..we are left at the mercy of teachers who dont have any intutive idea about calculus and thus they taught us with that limited knowledge .
Am i right that f(x) is basically length of the strip which varies with respect to x and and dx is common to which we multiply given f(x) If it is true then can we write f(x)dx.dx where first f(x) dx is area of one strip and next d(X) represents areas with respect to x
" dx is common to which we multiply given f(x) " dx is the width of each strip, as the video plainly shows. So f(x) times dx is the area of a strip. "next d(X) represents areas with respect to x" ????? I don't understand what this is supposed to mean. Is d(x) supposed to be a function d which depends on x?! But dx and d(x) then mean _totally_ different things.
Well, yes. He should've said that the width of the rectangles are Δx and not dx. Then, with Δx getting smaller, you get dx. Of course, the integral is just the limit of the Riemann sum
@@theoreticalmindsetThis video is just mind-blowing. Not only is the animation incredible, but the entire concept is fantastic. I've just started using Manim and have created a few animations, but nothing as good as this. Would it be possible for me to get the code as well?
beautiful, thanks for this
Nice visualization. :) But you should have included a remark that the integral symbol is simply an elongated S, representing the sum of all the rectangles.
Truly impressive visualisation.
Great choice of music
wow, beautiful, you helped me finally understand the mechanics behind it all!
it really helps a lot u deserves like👍👍
gods work has been done
Is there a way of visualizing the indefinite integral?
curious how did you "divide" those mobjects, aren't they in a VGroup?
could you be more precise?
did you use Manim?
btw, nice visualisation
yes i did. thanks
Here comes the 904th subscriber ❤
You're very welcome to the channel
I didn't get it , f(x) of each rectangle is different, so unless we calculate the area of each rectangle seprately .
How adding them all will give us area Under curve ?
Same confusion
I think f(x) is th the equation of graph. Say f(x)=sinx. and we are integrating this from a to b. so i think that is why....
"so unless we calculate the area of each rectangle seprately"
We indeed do that.
Gosh im in High School and stuff like this scares me lmao
u should be grateful..u are born in this era ..where such videos are there which could help anyone to understand difficult concept of calculus..back then when we are born ..we didnt have such resources ..we are left at the mercy of teachers who dont have any intutive idea about calculus and thus they taught us with that limited knowledge .
@@krishnenduray1758 👆
Am i right that f(x) is basically length of the strip which varies with respect to x and and dx is common to which we multiply given f(x)
If it is true then can we write f(x)dx.dx where first f(x) dx is area of one strip and next d(X) represents areas with respect to x
" dx is common to which we multiply given f(x) "
dx is the width of each strip, as the video plainly shows. So f(x) times dx is the area of a strip.
"next d(X) represents areas with respect to x"
????? I don't understand what this is supposed to mean. Is d(x) supposed to be a function d which depends on x?! But dx and d(x) then mean _totally_ different things.
Aren't these just Riemann's sums?
Well, yes. He should've said that the width of the rectangles are Δx and not dx. Then, with Δx getting smaller, you get dx. Of course, the integral is just the limit of the Riemann sum
Can I ask for the code for this video from you?
Of course, just shoot me an email and I'll send it to you!
@@theoreticalmindsetThis video is just mind-blowing. Not only is the animation incredible, but the entire concept is fantastic. I've just started using Manim and have created a few animations, but nothing as good as this. Would it be possible for me to get the code as well?
@@heligeonhd4538 Thank you! Of course, shoot me an email and I'll send it. Notice that the code from later videos are available at my GitHub.
To be honest the video is really good but I hope next time you choose something more fun and interesting, Keep up the good work
Thanks bro. Any specific topic you want me to cover?
@@theoreticalmindset Can you try to do any linear algebra?
@@skazzyeahh7710 Noted!
niceee, just dont use this music man,
gotcha
whatttt, I liked the music