Area between a curve and the x-axis | AP Calculus AB | Khan Academy
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- Опубликовано: 26 авг 2024
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Based on the fundamental theorem of calculus, we can use antiderivatives to compute integrals. Created by Sal Khan.
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Almost 11 years and you’re still helping students out 💯
why is this 5 minute video more informative than my two hour calc class?
I don't know how he does it I'm glad he does 😂
Everyone watch at 1.25x the speed. It is much faster and equally understandable. Good luck and God bless :D
me watching at 2x speed
@@jason.stevens Past me doesn't know what he's talking about. 2x is the only way to watch anything. 😉
@@ozzlicious you know it man 😂 100%
I've just got to say that you all are the biggest help in the whole world, thanks so much!
Within 5 minutes, it became so clear! Thanks!
Slowing it down to .5 makes him sound drunk. lmao
accurate
u right u right
ommg yeahh
that just alleviated my fear of definite integrals. I thought I had to evaluate it and get the sum of all values between the two numbers.
The sign for Integration comes from the LATIN LONG 'S' which essentially is short for Summa which in turn is short for SUMMATION which is what Integral Calculus is all about.
Leibnitz was the first person to use that symbol!!
The letters dx stand for INFINITESIMALLY SMALL particles of the variable x in this case
Hope this helps.
ty. the integral videos are superb and I'm having an easier time with this than limits themselves. is this usually the case for most people?
Made me learn it for about minutes..... OMG Commended Khan Academy!
Yeah me too, I never thought it would be possible to learn calculus and algebra in my class at the same time
Sal you are a lifesaver yet again!
Is there anything that I can do to help speed up the development of those integration practice exercises?
its cool that when you have f1(x)=ax/|x| and you have variable A for an equation, the y axes will be flipped where y : 1 => y : -1 and y : -1 => y : 1 *IF* the point is below x : 0
thank you very much
Here to study for a calc final tomorrow, anyone else?
Richard Maurice me
Same here.
SAME
test is in 2 hours, ye ye
I'm in 9th grade...
You should post more practice problems online. Post some Optimization and related rates problems that are three times harder than the AP exam.
Can you do a video on proving the area of a circle using integrals?
tried the equation on desmos it worked :)
Khan: 0:1 *&^%^&*&^^%^&*(*&^% 5:37
me: ammmm !!!????
khan : 5:38 sixty three over three, and three goes into sixty three exactly 21
me : finally some thing i know
When do you plug in functions then? Isn't that definite integration?
Sal I love u
My video about definite Integrals is exactly like this but with real paper
Wait what about the plus c's? Is it acceptable to discard them and not even write them out in this situation?
recursor94 my same question
I had the same question, but I think it's because the constant would cancel out. It would be the same for both sides of F(b) - F(a), so doesn't matter what it is, it would be gone!
I freaking love you
just a question though, where did you get f(x) = x^2 ?
It was the example
this lecture contain super logy and concept
You lost me at 3:43, where did that power rule come from?
Parodox306 it's the integral power role which is x^n+1/n+1
3:45 but is it not 2x instead of 3x^2? Also at the end he mentioned square units but exactly what square units?
At 3:45 I believe he took the derivative of x^3. Also the units can be anything, in the place of something like feet or meters you can just say units as none are specified.
Alef Nol look at the power rule when x^a. it ends up being (x^(a+1))/(a+1). end up as x^3/3+C
I love you 💕❤️
why dont we put c constant of integration
I had the same question, but I think it's because the constant would cancel out. It would be the same for both sides of F(b) - F(a), so doesn't matter what it is, it would be gone!
I love you
dx means what?
how did he get 64 again? My calculator does not have that
Someone say SIGMA?
I'm sorry, but am I the only one hearing a mosquito buzzing in the background (I have headphones on) I couldn't concentrate!!
Maybe it' s due to head phones ,just try to hear without headphones!
Im wearing earbuds right now and it's so uncomfortable how I can hear every splosh of your saliva and every sniff of your nose. It is so distracting.
Thanks for ruining Khan academy for me