Man I’m trying to learn first calculus, I was recommended this from a friend in the math field to help, it seems a bit to daunting, I wish I was I just good at math and actually understood what he is talking about most of the time
This video is amazing. I’m self taught, going through Professor Leonard’s Calc 3 YT series course, and double and triple integrals are coming up in the very near future so I wanted to get a head start. This is totally logical and it just makes sense
You can find both, the volume and the hypervolume of a tesseract. Although I think it's more difficult to grasp the concept of the volume of a tesseract
Brilliant , wish I had this when I did maths so much clearer and simple, during lock down going though my old notes 30 years ago inspired me to study more
Triple integrals don't calculate 4D hyperspace. They are just a different way of calculating 3D space when the area of the inside isn't increasing or decreasing linearly. You'd need a Quadruple integral to calculate hyperspace. Look it up for clarification. His reasoning sounds correct, but I double-checked it with a few sources, and they state that triple integrals only calculate 3D space.
The only thing is the first graph isn’t really a cube. The base is a square that is 1 unit on the x and 2 units in y but the height of the “cube” is the function of x and y. The way to think about it is like this, the integral uses the volume of a cube equation because in Cartesian coordinates that’s what it is. So like a cubes formula for volume = length x width x height, but here the function you are integrating is the height and the dx and dy values are the length and width of the base of the structure, the integrals limits form the base. Since the integral values are all numbers it forms a square but the height is variable based on the function. If it was just a normal cube the function you’d be integrating would be a number. What the integral is actually doing is creating an infinite amount of cubes all with different heights but the same base area dx dy and summing them all over the course of the square area projected out. The best way to picture it is to graph the function and then draw the square on the xy plane but then picture the square projecting upwards until it hits that function that’s the power of the integrals it allows you to take the volume of not a cube using the formula for a cube by just making infinitesimal cubes and adding their volumes together. What the total volume that we are finding is actually a shape that has a square base and the height is like a parabolic shape. The best way to picture it is to graph the function in 3d and picture the shape of the bounds on xy plane which in this case it’s a square and picture it’s height as the image of that square going up until it hits that 3d graph.
Was so thrilled when i did the double integral the other way from y/2 to (y)^1/2 and got the same answer! strangely that way took up less paper. Thanks for the solid content!
@lulu , your wicked tactics to paint real Christians ain't gonna work, people like you are the reason muslims conflate legitimate love lead criticism from people like David Wood and Robert Spencer with hatred from people like you and richard spencer.
You're an excellent teacher, you truly are. I survived 1st year of engineering with your help. It would be nice if you can make videos on differential equations 😅
Hi Professor Dave. I have a request that you may find interesting or not, it’s a mathematical one. I have always found it hard to understand “Inter-universal Teichmüller theory”, “The Collatz Conjecture”, and “The Birch and Swinnerton-Dyer Conjecture”. If you would make a video on one of these topics that would really help 😊 I’m studying a Master’s in mathematics in Denmark. I’m sorry for my English, I’m not mothertongue in English. Btw, I love your content.
Oh my god, thank you so much for this video. The videos that I get for my class gave me an example where both y and x's bounds were 1 so I didn't understand how she was doing it.
My doubt is the curve which has higher y value at particular x value should be considered higher curve. So it should lie close to y axis I think...@@m4rzb4rz-qq3yq
7:39 a mistake in limits integration of 2x and x² ? If 2x on the top and x² under of 2x => if x:1. 2(1),(1)² and if x:2 2(2),(2)² and if x:3 its undefined[ 2(3),(3)³] => 6,9
Best explanation around. Though im still struggling to understand how taking the integral of the x-y plane in two different ways gives volume. So the area under the curve given from the first integral just happens to also equal the volume?
In the example starting at 2:21 does this not just find the area of the surface in the x-y plane that is under the cube? I thought you would also have to integrate dz from 0 - z in order to calculate the volume of the shape?
hello can explain how you take x^2 as the lowest value for a integral and another integral. what makes them the upper value on y and lowest value on x ?can you make it more clear cause i tried to find why but still cant find out . At first i thought it was cause the 2x function was above the x^2 from 0 to 2. thanks you
If you look at f(x,y) = 1+ 4xy example, if you just look at solid by itself and compute volume without using complex integration, for x = 1 (1-0), y = 2, (3-1), and z = 1 + (4*1*2) = 9, I get a volume of 1*2*9=18. Where did I got wrong?
You are such a great teacher.
And I like how you use "we" instead of "you". Makes the student feel like they are not alone.
I think it's great because even the professors still are students at the end of the day, because everyone is still learning more about their subjects.
this is the clearest explaining math video i've ever watched
Ikr
Best teachers so far: 3blue1brown and Professor Dave.
You seriously wouldnt count sal or Patrickjmt?
Blackpenredpen
Professor Leonard is the best for me, by far
Zach star
For me, the best teachers so far are: Professor Gross, from MIT OCW Calculus Revisited, 3blue1brown, and Professor Dave
I was struggling a lot on understanding double integrals on a homework assignment, but this helped massively. Thanks Dave!
Blessings upon you, Dave. Two minutes in and you’ve already made this make more sense than my instructor.
Man I’m trying to learn first calculus, I was recommended this from a friend in the math field to help, it seems a bit to daunting, I wish I was I just good at math and actually understood what he is talking about most of the time
Start the calculus playlist from the very beginning and all will make sense!
This video is amazing. I’m self taught, going through Professor Leonard’s Calc 3 YT series course, and double and triple integrals are coming up in the very near future so I wanted to get a head start. This is totally logical and it just makes sense
Thanks, I checked out the series after seeing your comment. It is more suited to what I am looking for. Really appreciate it man.
This was simply amazing. I have never seen a TH-cam teacher be that clear and easy to understand. Thank you soooo much!!! :D
This video is better than 1 hour of lecture. Tq very much
Great explanation!
Of course, my inclination is still to hit it with a FOR loop...
I have a test tomorrow, and your video really helped me to understand integration more deeply. Thanks from Russia!
So you can actually find the volume inside a tesseract niceees
its a hypervolume
@@kek3324 It's*
Jorge C. M. I can tell you have a lot of friends.
It’s just all the side lengths multiplied
You can find both, the volume and the hypervolume of a tesseract. Although I think it's more difficult to grasp the concept of the volume of a tesseract
Brilliant , wish I had this when I did maths so much clearer and simple, during lock down going though my old notes 30 years ago inspired me to study more
I still don't understand why someone can dislike a video like this :( You are incredible!
th-cam.com/video/IangXACFW48/w-d-xo.html
I've finally done it. Thanks for your help, my good sir. I'm a lot more confident now.
Hi Dave, I got confused in the part choosing lower bound and upper bound between 2 cuves. Pls explain..
This is probably the best that this video could possibly have been made.
wow i didnt expect integrals to have this much depth to them... how can you not love math, omg
great video btw :)
Triple integrals don't calculate 4D hyperspace. They are just a different way of calculating 3D space when the area of the inside isn't increasing or decreasing linearly. You'd need a Quadruple integral to calculate hyperspace.
Look it up for clarification. His reasoning sounds correct, but I double-checked it with a few sources, and they state that triple integrals only calculate 3D space.
The only thing is the first graph isn’t really a cube. The base is a square that is 1 unit on the x and 2 units in y but the height of the “cube” is the function of x and y. The way to think about it is like this, the integral uses the volume of a cube equation because in Cartesian coordinates that’s what it is. So like a cubes formula for volume = length x width x height, but here the function you are integrating is the height and the dx and dy values are the length and width of the base of the structure, the integrals limits form the base. Since the integral values are all numbers it forms a square but the height is variable based on the function. If it was just a normal cube the function you’d be integrating would be a number. What the integral is actually doing is creating an infinite amount of cubes all with different heights but the same base area dx dy and summing them all over the course of the square area projected out. The best way to picture it is to graph the function and then draw the square on the xy plane but then picture the square projecting upwards until it hits that function that’s the power of the integrals it allows you to take the volume of not a cube using the formula for a cube by just making infinitesimal cubes and adding their volumes together. What the total volume that we are finding is actually a shape that has a square base and the height is like a parabolic shape. The best way to picture it is to graph the function in 3d and picture the shape of the bounds on xy plane which in this case it’s a square and picture it’s height as the image of that square going up until it hits that 3d graph.
whenever my dad checks up on me if im doing work, i just pull up your videos and he doesnt question it! thank you :D
A learner from Tanzania,🤝you are a good teacher ❤
Thank you for the subtitles in English! It makes it much easier to follow-up.
Thank you, that was one of the most straightfoward explaination!
Finally I understand the sense behind these
no word to explain your efforts may God reward this
Professor Dave, thank you so much for these resources! They've been a huge help to me in ODELA and Vector Calc. I'd be lost without you!
Was so thrilled when i did the double integral the other way from y/2 to (y)^1/2 and got the same answer! strangely that way took up less paper. Thanks for the solid content!
Thank you sir for your dedication and for making this free! 🙏
Can you do a video on Green's, Stokes' and Gauss' Theorems?
Could you send me notes of divergence theorem ?
Millie all three of those are filmed, animated, uploaded, and to be released very soon!
@lulu , your wicked tactics to paint real Christians ain't gonna work, people like you are the reason muslims conflate legitimate love lead criticism from people like David Wood and Robert Spencer with hatred from people like you and richard spencer.
20UPH512_Geo Raphael Michael
What was lulu’s comment about?
@@GeoRaphaelMichael
*_Bruh, what_*
Integrals are the most usefull part of math. Engineering is the example for that. Love them.
Don't forget differential equations which model pretty much every dynamic phenomena
“Performing multiple integrations is not all that daunting, on the SURFACE!!” Haha
Integrals are tight. You made it look super easy, barely an inconvenience.
You're the E of the mc²! Great lecture. Congrats.
You're an excellent teacher, you truly are. I survived 1st year of engineering with your help. It would be nice if you can make videos on differential equations 😅
14:30 The first example on the Checking comprehension is wrong: the internal integral boundaries should be from x+1 to 2x
annnnnnnnnnnnnnd you have a new sub/ bingewatcher
Thanks so much! I never understood this in my Engineering lectures, now it makes sense.
Hi Rosal.can I know is this thing involve I'm grade 12 or higher grade .Because I'm going to do engineering too. Currently grade 12
OsJ I’m not sure, I studied this in university.
Thank you for the videos. They help a lot! I’ve had a mental block about these topics for decades.
I wish i had u as my teacher during my btech...
So clear and comprehensible. Thanks!
I thought that double integrals give the area of the surface of a function and triple integrals the volume of a function respectively
Και εγώ ρε φίλε,έτσι δεν λέει και ο γκαρουτσος? 😂
Don't they?@@tzonic8655
that is amazing how clear you was
Hi Professor Dave.
I have a request that you may find interesting or not, it’s a mathematical one. I have always found it hard to understand “Inter-universal Teichmüller theory”, “The Collatz Conjecture”, and “The Birch and Swinnerton-Dyer Conjecture”. If you would make a video on one of these topics that would really help 😊
I’m studying a Master’s in mathematics in Denmark. I’m sorry for my English, I’m not mothertongue in English.
Btw, I love your content.
In the first comprehension, when we move from 2 to 3 in x,then y=x+1 is lower to 2x . Why we consider here limit in y from 2x to (x+1)?
8:26; why is Y (upper bound) = x ^2.
Why choose x^2 over 2x.
----------
And X upper bound =2x.
Why choose 2x over x^2?
I appreciate the answer☀️
because x^2 is of greater value, duh
Why is the y integral from x^2 to 2x and not 2x to x^2?
Lower relative to y
1:37 I think there are counterexamples to that statement, but it works in general.
Could you tell pls
Oh my god, thank you so much for this video. The videos that I get for my class gave me an example where both y and x's bounds were 1 so I didn't understand how she was doing it.
Actually at 8:34, we get x = ±√y, x = -√y being the other half of the parabola. So we write x = √y .
I consider the view count on this an insult. And an even greater one, that 52 people dare dislike it. Dave, your videos are amazing.
How do you know it goes from y=x^2 to y=2x why is one the lower curve and the other the higher curve?
Hope it's not to late. Look at the x axis, the one closest to it is the lower one
@@m4rzb4rz-qq3yq no, not too late😅, thank you very much!
@leowalentiny1638 no problem :)
My doubt is the curve which has higher y value at particular x value should be considered higher curve. So it should lie close to y axis I think...@@m4rzb4rz-qq3yq
I don't understand which would be the lower curve and which would be the higher curve?
Thank you, so much
good job Dave, you have explained this to me in a most understandable way possible, with clear color indications, thank you sir.
Thank You very much.
But, what do you mean by lower curve to higher curve while setting the bound?
We have a calc quiz tomorrow and this video sure helps, Thanks!
Danke sehr!!!
🎊 beste Erklärung! Mit Abbildungen, klar und deutlich.
❤❤❤❤❤
at 07:12 , how do you say that y runs from the lower curve to upper curve? sir i cant understand that point
A video masterpiece. Grateful for the illustrations, painted a clearer picture in my mind...
I have a question please
For the upper and lower bounds isn't the x² greater than 2x and why didn't it get placed at the upper bound instead?.
7:39 a mistake in limits integration of 2x and x² ?
If 2x on the top and x² under of 2x => if x:1. 2(1),(1)² and if x:2 2(2),(2)² and if x:3 its undefined[ 2(3),(3)³] => 6,9
cool teacher, straight to the point
I dont understand what he meant by lower curve and higher curve when setting the bounds at 7:08
Best explanation around. Though im still struggling to understand how taking the integral of the x-y plane in two different ways gives volume. So the area under the curve given from the first integral just happens to also equal the volume?
But can Professor Dave explain why my prof throws trigonometric bounds on the triple integrals like wtf why do you hate me
Great video. Even though I only did high school calculus I could still follow what he is saying.
I was only confused in one step it got cleared only within first 2 minutes...
There is an error at 10.55. In the equation , it should be 2xpower4 not"8xpower4. Therefore the volume is 24. It is not a negative value
No it's good.
@@rashikasookun3907 Ya. I just made a silly mistake.
idea, you could create a new notation where a single integral sign is arc length, double is area and triple is volume
You getting people through college
Is there any video that shows how integrals are applied in engineering, for example, for building a bridge, a dam, a building, etc?
now this is what math should be about. Solving something real
In the example starting at 2:21 does this not just find the area of the surface in the x-y plane that is under the cube? I thought you would also have to integrate dz from 0 - z in order to calculate the volume of the shape?
KING
blessings upon you, Dave.
finding boundaries are the hardest part
If the double integral of the absolute value of f is finite: the order doesn’t matter: the double integral of f is the same regardless of order
hello can explain how you take x^2 as the lowest value for a integral and another integral.
what makes them the upper value on y and lowest value on x ?can you make it more clear cause i tried to find why but still cant find out .
At first i thought it was cause the 2x function was above the x^2 from 0 to 2.
thanks you
You're right, depends on the sign. Solve sqrt(y) >= y/2, it's true on [0; 4].
I wish we had you as our professor
I need more details in triple integrals, it is hard to imagine in 4D
It is impossible to imagine a 4d space literally
oh men i wish i knew you back when i was taking Applied maths 2 in college
Great Visualization of the figure formed by double integration
Loved it !!
Thanks for making calculus fun and interesting
Wow that was easier then expected. Thank you for explaining it well.
He does know all about science stuff......... professor Dave Explains ❤️❤️❤️🔥🔥🔥. I Love this😎
Would love to see some diff eq stuff. You’re so easy to learn from
coming soon!
@@ProfessorDaveExplains I’m so excited. I’ve been on a math kick
I thank you dear sir for mentoring me . 🙏
Can someone please explain why the curve y=2x is greater than the curve y=x^2? Thanks in advance!
Is there a way to generate the f(x,y) equation knowing only the two equations y=x^2 and y=2x? I don't see the connection between these.
Both of those examples are only 2-dimensional equations. You would need a 3-dimensional equation to determine f(x,y).
Wanted the computation process for the two problems.
awesome vid thanks im a fresher ive jusst started self learning ths topic ths will help wth understanding
Hey dave can you graph this function in 3D f(x,y)=xy/(x^2-y^2) around the point(0,0)
love you professor dave
what if the functions defining the bounds overlaps more then once? Like sin(x) and x/2 then how do you determine the lower and upper bound?
Ooh that's a good question. I suppose in such a case you would split it up into multiple integrals.
excuse me prof, why my answer evaluate 1 is -3/2, where i'm wrong?
Great thought and too clear fellow style, I apricate your way of explains
If you look at f(x,y) = 1+ 4xy example, if you just look at solid by itself and compute volume without using complex integration, for x = 1 (1-0), y = 2, (3-1), and z = 1 + (4*1*2) = 9, I get a volume of 1*2*9=18. Where did I got wrong?
Really nice ... So clear concept.... Thank you professor Dave
I don't know why I need to pay to go in the Uni after this video
So they give you a paper stating your watched some yt videos