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
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
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
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
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
@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.
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!
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.
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?
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.
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.
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?
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 😅
Thank you so much! I really appreciate this as we don't get taught a lot of concepts and underlying principles in math, so this just makes the subject so much more interesting. :)
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
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.
why is the equation at 3:40 (z = 1 + 4xy)? the diagram just looks like (z = height of rectangular prism) to me. the more i think about it the top of the object should equal 1 at the y axis, and at x=1 should be a line with slope 4 going from h = 5 to h=13. in other words a weird slanty surface and not a plane. yeah, I just put z=1+4xy into my graphing program and it was this parabola thingy with four asymptotes. not flat within any bounds. ???
If we look at the graph, the curve y=x^2 is closer to the y-axis hence being lower while the curve y=2x is farther from the y-axis hence being the upper bound. Another way of checking that is by putting values in the curve equations. As X runs from 0 to 2, putting 1 in the equations gives lower value on y=x^2 so it is chosen as the lower bound. Also, if you start from the x-axis and then continue going up to the y-axis, the first line you would hit will be y=x^2 hence that is your lower boundary and the second line you would hit would be y=2x hence that would be your upper boundary.
this is the clearest explaining math video i've ever watched
Ikr
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.
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.
This was simply amazing. I have never seen a TH-cam teacher be that clear and easy to understand. Thank you soooo much!!! :D
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
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.
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!
Great explanation!
Of course, my inclination is still to hit it with a FOR loop...
This video is better than 1 hour of lecture. Tq very much
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
14:30 The first example on the Checking comprehension is wrong: the internal integral boundaries should be from x+1 to 2x
“Performing multiple integrations is not all that daunting, on the SURFACE!!” Haha
Hi Dave, I got confused in the part choosing lower bound and upper bound between 2 cuves. Pls explain..
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
1:37 I think there are counterexamples to that statement, but it works in general.
Could you tell pls
wow i didnt expect integrals to have this much depth to them... how can you not love math, omg
great video btw :)
Thanks!
I dont understand what he meant by lower curve and higher curve when setting the bounds at 7:08
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_*
I have a test tomorrow, and your video really helped me to understand integration more deeply. Thanks from Russia!
Thank you, that was one of the most straightfoward explaination!
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
Why is the y integral from x^2 to 2x and not 2x to x^2?
Lower relative to y
I've finally done it. Thanks for your help, my good sir. I'm a lot more confident now.
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
annnnnnnnnnnnnnd you have a new sub/ bingewatcher
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)?
This is probably the best that this video could possibly have been made.
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
Finally I understand the sense behind these
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!
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!
at 07:12 , how do you say that y runs from the lower curve to upper curve? sir i cant understand that point
Thank you sir for your dedication and for making this free! 🙏
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
Thank you for the videos. They help a lot! I’ve had a mental block about these topics for decades.
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.
Actually at 8:34, we get x = ±√y, x = -√y being the other half of the parabola. So we write x = √y .
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 subtitles in English! It makes it much easier to follow-up.
You're the E of the mc²! Great lecture. Congrats.
I wish i had u as my teacher during my btech...
So clear and comprehensible. Thanks!
good job Dave, you have explained this to me in a most understandable way possible, with clear color indications, thank you sir.
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
A learner from Tanzania,🤝you are a good teacher ❤
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
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?.
that is amazing how clear you was
A video masterpiece. Grateful for the illustrations, painted a clearer picture in my mind...
Integrals are tight. You made it look super easy, barely an inconvenience.
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?
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.
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.
no word to explain your efforts may God reward this
But can Professor Dave explain why my prof throws trigonometric bounds on the triple integrals like wtf why do you hate me
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?
Danke sehr!!!
🎊 beste Erklärung! Mit Abbildungen, klar und deutlich.
❤❤❤❤❤
I was only confused in one step it got cleared only within first 2 minutes...
I don't understand which would be the lower curve and which would be the higher curve?
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 😅
my dear, i finally understand that thing!! u save me!! thank you very very much!!
Thank you so much! I really appreciate this as we don't get taught a lot of concepts and underlying principles in math, so this just makes the subject so much more interesting. :)
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
Wow that was easier then expected. Thank you for explaining it well.
Really nice ... So clear concept.... Thank you professor Dave
Great video. Even though I only did high school calculus I could still follow what he is saying.
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].
Great Visualization of the figure formed by double integration
Loved it !!
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.
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.
We have a calc quiz tomorrow and this video sure helps, Thanks!
now this is what math should be about. Solving something real
I don't understand when it's lower or upper bound. I'm guessing it's whichever function has a larger area under the curve?
Can someone please explain why the curve y=2x is greater than the curve y=x^2? Thanks in advance!
14:47 I got 6x^2 when I substitute 2x to the derived equation for y...
cool teacher, straight to the point
Nice work... You deserve a big big big thanks... Go ahead Dave brother
Thank You very much.
But, what do you mean by lower curve to higher curve while setting the bound?
awesome vid thanks im a fresher ive jusst started self learning ths topic ths will help wth understanding
Is there any video that shows how integrals are applied in engineering, for example, for building a bridge, a dam, a building, etc?
blessings upon you, Dave.
You getting people through college
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
Thats the most outstanding explanation I ever got. Thank you so much!
why is the equation at 3:40 (z = 1 + 4xy)? the diagram just looks like (z = height of rectangular prism) to me. the more i think about it the top of the object should equal 1 at the y axis, and at x=1 should be a line with slope 4 going from h = 5 to h=13. in other words a weird slanty surface and not a plane. yeah, I just put z=1+4xy into my graphing program and it was this parabola thingy with four asymptotes. not flat within any bounds. ???
Thank you, so much
How did you decide that x^2 is the smallest bound not the 2x?
moving in the positive y direction, starting on the x axis, you hit x^2 first, and then 2x.
@@ProfessorDaveExplains than ks
If we look at the graph, the curve y=x^2 is closer to the y-axis hence being lower while the curve y=2x is farther from the y-axis hence being the upper bound.
Another way of checking that is by putting values in the curve equations. As X runs from 0 to 2, putting 1 in the equations gives lower value on y=x^2 so it is chosen as the lower bound.
Also, if you start from the x-axis and then continue going up to the y-axis, the first line you would hit will be y=x^2 hence that is your lower boundary and the second line you would hit would be y=2x hence that would be your upper boundary.
@@ProfessorDaveExplainsThank you so much professor for this explaining ❤
@@sourashian5901Thank you too for your deeper explaining ❤
Thanks for you explanation I understand well
love you professor dave
Thanks for making calculus fun and interesting
Great thought and too clear fellow style, I apricate your way of explains
oh men i wish i knew you back when i was taking Applied maths 2 in college
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).
Thanks so much for a clear presentation.
4:20 wow it seems you answering me the solution of the question which i asked in other's videos of same topic but of basic
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.
Hey dave can you graph this function in 3D f(x,y)=xy/(x^2-y^2) around the point(0,0)