Integration : What is an Integral
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- čas přidán 28. 08. 2024
- In this video I introduce the concept of an integral for the first time. I feel that in school etc., people are not told what an integral IS but rather how to compute an integral. I think that is the wrong way to go about doing business, so here i go, enjoy!!
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Bro i am in 8th grade and still understood this teacher deserves to be titled after the best teacher ever
I'm a grad student from a non-STEM field, taking an engineering class as an elective, and I'm baffled by the math. Your videos are the clearest and most helpful I've seen, and are such a relief! Thank you so much!
Adam Beatty, your explanation to Integrals has surpassed that of my professor. Very clear and helped tie everything together. Thank You very much!
.....You are right!!!! When these subjects are "taught/introduced" in school, they ALWAYS SEEM TO FORGET to SHOW WHY WHERE, WHEN and HOW this type of mathematical "solution" IS ACTUALLY USED!!! => WHAT IS THIS ALL to be USED FOR???!!!.... [BTW: Thank you, Adam!]
Honest to God you are the best teacher ever I had learned from. Please keep posting more .
Youre an incredible teacher. Very smooth lesson.
Thank you very much! Glad I can help!
Thank you so much for this. I've found over and over again in Math classes that I'm taught how to find things but not what something actually is. This helped my understanding of everything I've learnt so much
Thank you! You are the only one who went in depth and explained what an integral actually is! You're the best. If you haven't already could you please make a video about the Integral properties and rules? Thanks again!
This is the best explanation of integration you will find on CZcams guaranteed.
Thank you very much! You are an excelente teacher! Now, after many years, it is clear to me. A light in the dark....
thank you very much for this video....my calc professor just threw integration at us and I had no idea what we were even doing
Thank you, Professor Beatty! You really made integrals very clear!
I took calculus 1 on derivatives and integrals 2 years ago and now Im taking calculus 2 and I dont remember nothing thats why I'm here. But I still remember stuff from accounting and economics because they made sense to me in real life. We should know the use of all these techniques so we wont forget them fast.
You have a gift for teaching. Thank you very much.
Thank you for your kind feedback!
Why didn't my calculus teacher in college start with this lesson? Concepts that were fuzzy for a long time are now clear.
Glad to hear!!
@Kreso2577 PART 1 . Think about what an integral does. It gets the area under a curve, or it adds up all the 'y' values of each 'x' value. So say we start at x (get the y value) and move to x+1 (add this y value to the previouse one) move to x+2 and add this y value and so on. Here our increment is 1, this is our dx. However, we are missing all of the middle values like x+0.00003 or x+.7 etc. so if we make a smaller increment , a smaller dx, we would get a better estimate on our integral.
Thank you for this video...im tired of just being told in school how to do stuff...without them really worring if we know know exactly what what we're doing means. THANK YOU SO MUCH!
Thank you for the explanation, clear and simple...
Thank you very much. I realise after many years that my foundation in integral is not that solid. thank you again
@Kreso2577 PART 2. So to get a perfectly accurate integral, we want our increment, our dx to be as small as possible. so we let be as small as possible
to be honest, i've never seen limits like that. but if you look, the upper limit is x^2 and you're being asked to evaluate its value at x=2, so the upper limit is 4. why it says F(4) i'm not sure, maybe you're missing some information or it's a different notation than I'm used fto for integrals. the integral is pretty simple, it's a natural log. so you've got ln(....)/d/dt() where ()=4sqrt(t) +1
the derivative here is [4*t^(3/2)]/(3/2) + t. I got 0.18 as the answer.
Good video. It's nice that I found it because that's my biggest complaint with how they taught us integrals. They show you how to do one, but they leave you with absolutely no explanation of what they are used for. No wonder some people have this idea that math has no use in the real world. It's not very memorable to learn something without knowing WHY. Thanks.
YESYESYES! From beginning to end, you have helped me.
Now I won't fail maths tomorrow. Thanks :)
@jjjeahh awesome cheers, i didn't know that at all, oftentimes introducing something new is best done by being partially correct
You are actually helping me in maths. I subscribe.
Mainly in university, I was never particularly good at it in school though!
Great stuff! Thanks for the positive feedback!
Very helpful & clear explanation of integral applications. It always helps to know how mathematical techniques can be used. Thanks!
with all honesty you are brilliant and amazing. why? because, you explain very well, make it VERY easy ... Thank you !
Thanks. I'm being thrown into the deep end of probability theory, and this filled in some gaps for me very well.
thanks. im trying to learn physics completely on my own
thanks for your videos, i'm learning English and they're very helpful and interesting for me))) slow speech rate and easy examples))) thanks a lot)))
this is great, i wish courses were more cut and dry like this. we had to do all sorts of nonsense and computing riemann sums and the like before we ever got to the concept of integrals. it just seems as if we were taught all these things we don't need to know to understand a concept that's not all that difficult to understand in the first place.
this is beautiful. Thank you!
sorry if i'm wrong but at 9:16 dy/dx= 6x is false, because dy/dx should equal to
y1-y2/x1-x2
in your case you assumed y1=y2=y or x1=x2=x so your answer was 3x+3x when the real answer is 3x1+3x2
you sir deserve an oscar
very well explained. Thank you :)
Excellent video and this man's Irish guys, not Scottish :P
And you will also need to use endless amounts of integrals in economics when trying to analyse profit margins and macroeconomic objectives.
better than the mit video. thanks great info.
you are good.....very good...especially for someone as slow as me lol. That was amazing, i fell in love because you made someone like me (unteachable), teachable, and i left with some knowledge! WOW!!
#Magic
Its so frustrating i go to school to learn but they are most interested in me just turning into someone that memorizes formulas.
beautiful explanation.
Nope, the derivative is correct alright. Remember, y2-y1/x2-x1 is the slope. The derivative is the instantaneous rate of change; it's the limit of the slope as you shrink x2-x1 to zero. If that doesn't make sense don't worry
How is integration applied to a cylinder or cube or other three dimensional structure? I think of it as follows:- You are given a very thin transverse slice of a cylinder and by using integration you work out the whole volume of the cylinder. Differentiation is the opposite. You are given the whole cylinder and you work out the dimensions for the slice .Is this correct?
Always start with either a substitution or by parts. They will work for almost every integral you encounter in school. In this case, a substitution should work
Aren't velocity v time graphs showing acceleration, not distance?
+Jake Ingram yes, it shows them both the line shows acceleration and the area under the graph shows the distance
+D.K. kornima ah, ok- I forgot about area
Bless you sir.
I am just researching and appreciate the explanation at least up to 3:03. I am trying to understand how to calculate the MOI of an irregular body that is balances and will rotate about an axis. Inventor will provide a number but I am told that it is not accurate. One of my resources spoke of integrals. I have never had calculus and as a result I am a bit out of sorts. Thanks again.
thank you so much it was really nice , I learn to much and the meaning of integral
you can't FIND THE EXACT AREA under a curve if you're taking the "INDEFINITE INTEGRAL" of something...because the stuff under the curve is INFINITE.
However, you can find the exact area under a curve (and not have an equation or anything) if YOU'RE TAKING A DEFINITE INTEGRAL. If you're taking a definite integral, you basically have 2 points to take the area from.
Hope that clears things up.
Great vid, thanks man!
Thank you for the explanation!
You're welcome!
Very helpful. Your expertise is great. How long have you been studying mathematics?
Great video man
cool stuff!!!
Superb.
so helpful; thank you
thanks bud, eventually this made sense to me
That was awesome
Thank you for your kind feedback!
Thank you so much
Could you please keep few more videos on physics topic.
excellent - difficult subject clearly explained
So that's what integrals are for. Im already in cal 2, and ive yet to understand what the hell of integrals are for. I know how to do it, but as to what it is used for in the real world? I had no idea until now. Thanks man.
Same here! For Calc 1, we know the meaning of differentiation, which is the rate of change. But what's integration? Did you find out? Like what you said, I know how to do it, but I don't understand the concept and the meaning of it. I know definite integrals is the area, but what about just antiderivatives themselves?
You're very welcome!
I wish this video would have gone more in depth into what an integral is and how to do one.
cool stuff.. but now you have me wondering ... if differentiation is the opposite to (integration = adding) then is differentiation simply subtracting? Actually I've been learning differentiation and I've been trying to work out on my own, "the hidden factorial like formula that works out the area under the curve.".. awww and now you just spoiled all the fun. :) thnx. Argh.. and it was staring us in the face the whole time, of course the exponential function to the linear function is describing the accumulation under the line. Or at least half of it.
hey quick question dx is what exactly? and alittle hint make sure all your stuff being showed shows up on camera
thanx ......I was really cofused about integral :P
get lost
area under the curve represents Displacement
you are forgetting sections of the curve that dip below the x axis...
Thank you
this helped SO much thank you
Bless you
6x=Seks, dx=Deks --------- integrating Seks and Deks = 1/SeksDeks = DeksterSekster
thank u!!
Thnx!
Thanks for the clarifying. Would you please tell me what are those math prerequisites knowledge I need to learn before coming up for this session (integral)?
bcz within your teaching I couldn't take some of your points due to lack of enough math knowledge. Do I need to learn some trigonomy before or what else? really appreciate you. cheers.
This is usually taught at the end of the Calculus 1 course, so the only prerequisite (if any) would be pre-calculus.
Many thanks Andr ! clear enough. Cheers mate.
so i use integral to calculate area underneath some function...why would i do that, what that area represents, what can i do with it?
thx sooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo much!!!!!!!!!!!!!!!!!
When it says find F(4) when x=2 integral from 0 to x^2 of 1/(4root(t) +1) how do u do that?
Really helpful, Thank you!
An integral isn't always the area under a curve, though. The integral of sin(x), for example, does not give you the area under its curve. It can be used to find the area under the curve, but it is not by itself the area under the curve. And what about the constant of integration? An integral can't be the area if there's some indeterminate constant added onto it. So after watching this video, I'm still left with the question: what is an integral?
+Kyle Delaney Hi Kyle, those are great questions - perhaps a bit beyond the scope of this video. The integral of sine does give the area under the curve, but the direction matters. The curve is split, evenly, above and below the x-axis and therefore the positive area and negative cancel. That's why it integrates to zero (over an even region). Try integrate sine from 0 to 180 degrees, it's non zero ( or even 0 to anything 0
Yeah, my confusion had nothing to do with the negative area under the x axis. I already knew all that. It's just that without the constant of integration, that integral of sin(x) is -cos(x). So the values you gave in that link were wrong, since -cos(360 degrees) = -1. The area under the curve of sin(x) is -cos(x)+1, right? So my questions sort of answer each other then. If integrating sin(x) gives -cos(x)+c, then that could very well be -cos(x)+1, right?
I guess what you were doing in that Twitter post was partial integration. To get 0, you'd have to subtract -cos(0) from -cos(360 degrees). But that's what led to my initial question. If in order to find the area under a curve you have to subtract one integral from another, then what is just one integral by itself?
Thanks :)
There are many ways to visualise integration; one of those is as you say
thanks
Glad you liked it!
at last i know where i can use this
(x^(2)/4)*(sqrt(x^(2)+4)) dx...
can you please help with this integration?
I say that at 7.01
what's physics like in university? I'm currently in 6th year and don't have a clue what to do after school! I enjoy applied maths and physics in school but I have a useless teacher that cannot explain even the most basic concepts :/
lol. amazing .. i can't believe given my occupation i didn't know this
Nice
y = -3x^2 not 3x^2 in that graph
I thought the opposite of integration was derivatives
please explain it with an example i did not understand in the above example about velocity and time you explained the area under the curve but HOW COULD I GET THE DISTANCE TRAVELLED in that time and in the second example of y=f(x)=3timesxsquare at first you took values for x and in the end you did not take any values or limits .SO PLEASE EXPLAIN IT WITH A PROPER EXAMPLE
Thanks for your question. Think about distance, speed and time again. If you're in a car, then provided you know how fast you traveled and how long you drove for, you can calculate the distance you traveled. I.e., distance = speed x time. But if the speed is constantly changing, then you would have to compute the segments traveled at each different speed. I.e., total distance = distance at speed 1 + distance at speed 2 + distance at speed 3 etc. Distance at speed 1 = speed 1 x time at speed 1. Distance at speed 2 = speed 2 x time at speed 2. Distance at speed 3 = speed 3 x time at speed 3. A quicker way to do the same calculation is to integrate speed with respect to time. I.e., Total distance = ∫ v(t) dt. I hope this helps, you'll have to look somewhere else if it doesn't. Happy studies!
in theory its ok but explain it with an example in which would integration and the formula based calcuation is nearly equal
in theory its ok but explain it with an example where both calculation and integration are nearly equal
Hi Amar, I'm confused. The distance traveled example is exactly that. Can you rephrase the question please
i mean with a numerical example taking velocity as a function and time as variant. as i am able to know that that the change in time dt always remains the same but the velocity is always varying so that we are able see a curve in that example but if you could explain it to me numerically it would be better understandable
Yet another video explaining something very clearly in 10 minutes that teachers either hopelessly struggled with, or didnt bother to convey with enthusiasm 40 years ago.
Yep, thats how dry UK high school education was in the 1970s, total waste of time!
it still is.
4:00 y=-3x^2?
y=[-3 (×-4)^2]+4
im still in high school but i saw it on many equations whenever i was bored and looked them up on the web. now i know what they mean (atleast that :P)
ah a familiar accent :) im home
he's irish!
It may just be because I'm 13 but I didn't get this at all.
Thanks for your feedback. I'm sorry I couldn't help
I am gonna kick my math teacher for not teaching this 4 me....SALAM