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Calculating Double Integrals over General Regions
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- Опубліковано 9 кві 2008
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Calculating Double Integrals over General Regions - Two complete examples are shown. For more free math videos, visit PatrickJMT.com
this was uploaded almost 11 years ago. Crazy to think that the people who firstly watched this video is now probably a licensed mathematician,engineer,is in the business world, or even dead. I was only in 2nd grade when this was uploaded, now im a freshmen college. Holy fck
dang I was in first grade or kindergarten
This video brings me back
I am here in 2021 in my first year of college and Im watching this now XD
When this was uploaded, I was in kindergarten. Now, I'm in my second year of university.
did u graduate already
The video really helps. Btw at 8:45, it should be x^4/2 instead of x^4/4
Bless you! Who knows how many engineers, physicists, statisticians, chemists, etc. you have helped. You the real MVP, Patrick. Thank you!!!
Your are prolly an engineer by now
@@AjaySharma-dl7uy I build and deploy statistical models for forecasting product demand (supply chain) funny to look back at this comment. Things have gotten a lot better.
@@BombedNevada oh man ! Do you have an Internship position available lmao
Dope how math and physics haven't changed since 2008. These videos should be able to help someone from the year 2123
Silvanus P. Thompson, F.R.S wrotes in "Calculus made easy, 1914,
"Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the text books advanced mathematics-and they are moslty clever fools-seldom take the trouble to show you how easy the easy calculations are. On the contrary they seems to desire to impress you with their tremendous cleverness by going about it n most difficult way".
Thank you so much! This old video right here helped me through how to find the limits to calculate continuous random variable joint probability density function. Thank you again!
Hot damn patty, youve done it again! Teach me in 5 minutes what my prof couldnt teach in 5 hours. Like a boss.
What I hate about teachers is they teach and quote everything out of the book. They don't take the time to make sure students understand what the book is saying. That's why I rarely go to class because if they are just going to spend class time citing the textbook, I can do that on my own time. That's why I love Patrick's videos, they give real insight to what textbooks are trying to communicate.
Thank you so much. I understand my 3 hrs. lecture in about 10 minutes !
🙏🙏🙏🙏
That helped so much, thank you.
you wrote (x^4)/4 at 8:44 but shouldn't it be (x^4)/2 ??
Ya ur ryt he has mistaken somehow
sheesh though i was crazy
@@SNYPQuiCKsHOTS you still are tho.....
OMG.... I love you!!! This stuff scared me and confused me so much, but you make it easy peazy in 10 minutes or less.
As always, Thank you for the amazing video.
Thanks Patrick. U makes my college math easier. Im going to have my final next week. Btw, i already subcribed and liked the video. Looking forward for your other videos. ;)
my multivariable calculus teacher sounds like dr doofenshmirtz an jarjarbinks had a baby. i cant understand a word he says. thank you for this
@NicoThR, 3/10 is correct. The error that lead to 7/20 occured at 8:45, where there is a comment 'i write 4 in the denominator, but it should still be a 2.' It should be a 2, and with a 2 in the denominator you get 3/10.
Wow that was awesome, I am taking calc III this semester and I did the first integral myself after a few seconds and got the correct answer! Basically I jumped ahead several sections and did this; great job!
final ans` should be 3/10 i believe... (since he mis-wrote 2 as 4..)
Thank you for a lot of videos that help me get a cracked-open point to understand some concepts.
you are an amazing teacher ! I 'm studying my exams always with ur videos , short but meaningful
You are seriously the greatest person on the face of this planet.
ops, yes you are correct! i just added annotations so that everyone else will know!
thanks for helping!
I mean, the math is amazing but what's mind blowing is the fact you do all this stuff in sharpie and make like ZERO mistakes!!! great vid, Patrick.
you are very good at explaining this, i wish my calculus teacher was this good
you sir, are a freakin life saviour!
You are amazing I don’t know what I could do without u 🌺
Great video!
The best!! nothing else to say man, you are the best.
Excellent. I just realised that you when you get integrals in the form int x dy you can treat the x as a constant and throw it outside the integral before integrating whatever is left inside. Big aha moment - thanks very much!
Nice!!! That's exactly what every math student need
It really help me doing my homework, thanks a lot
You probally think i'm stalking you due to the number of videos that i say this on but here it goes again...THANK YOU! Also you are amazing and are the reason why i like math and am thinking of adding a minor in it. It's fun when its done right and there's a good teacher, like you, to teach it.
you are amazing pls keep making vids
@nikan4now in this, case it represents the volume below the surface and bounded below by the x-y plane
The answer to the second problem is 3/10. Patrick made a mistake at 8:44 by changing the 2 to a 4. It should be x^4/2.
in the first example when u replaced by u where do you take the numerator x??
thanks for the video it really helped me
Thanks for interpreting the specific procedures of processing fist and second integral. :)
You make calculus transparent!! Thank You!!
Thank you very much, Sir🙏🏼
Thanks dude, amazing how much study time you can save by watching a video.
i just noticed that too! i need to learn how to do some wide screen filming now
Man thank you so much!! I fail the topics you dont cover.
How do we know if it's easier to integrate with X first or y first?
thank u man really appreciated ur concern ur damn easy 2 understand
Thank god there were comments about the mistake. I was following along on the website, and when he got x^4/4 I was trippin for like 20 min trying to figure out what was going on lol. Not baggin on ya man. I thought I had done something wrong considering ur videos teach me most of what I know about this stuff.
mmm memories, im currently taking an electromagnetics course and we use a lot of double and triple integration, surface/line/volume integrals. fun stuff!
it is great thanks for the videos
thanks ,very helpful
Thanks a lot sir.
You teach better than my college teacher THANKX !!!!!!
You are a live saver!
can I subscribe twice? :) your video are so amazing.. there is nothing I can say but thank you so much.. Thank you for helping us..
May I ask, is there a list of drawn graphic regarding to any kind of solutions? I'm stucked at how to draw the graph when I get the question. Please help.
You saved my life man :D THX
Could you please drop a video on those jacobian what what.. i really like how u simplify things
this was so helpful
@patrickJMT Thanks Mate !I guess these people are just not willing to admit taht this was actually one of the best lectures about double integrals over general regions (:
THANK YOU SO MUCH SIR!!!! LIFE SAVER
the answer is actually 3/10 after the mistake was corrected
+Jaydev Thompson yes
yea np
Thanks for writing that down. I was already going to smash my screen after seeing the answer that Patrick wrote, lol.
Lol OK ...
I started to second guess my answer until I saw the comment, thank you :)
how do you find what to integrate? I don't understand how you get 2y/x^2 +1 from the region to integrate it.
Quite helpful, thx
you would evaluate just as if it were a constant. if it happens to have a variable left in the answer after your final evaluation I would suggest switching the order of integration or try using Fubini's Theorem
Hi Patrick, I was asked to do a similar problem in a recent exam. I was asked to do the double integral of x over some limits and was shown a rectangular shape on the graph, from which I had to set the limits myself. My question is, does it not matter what expression you are asked to integrate?
simply u made it easy.. thanx
really helpfull video..just made ny day (:
Patrick ... I really wish you were my Math teacher .. I think my life would have been so much easier ! =D ... Thanks for your great vids :)
thank you for everything
buen aporte. its a great video, thank you very much.
@patrickJMT Ok, no problem at all =) I was just curious. Thanks for your comment and for everything you do. I really appreciate all of your videos!!!! I would be completely lost with out your help!! You are so awesome!!!!
Thank you sir
great! thank u mate!
@MrKyte12 ha, you can try : )
Only because I didn't see it in the top 10 comments but on the last equation he doubled the denominator when he did the last part of the first integration which makes the last problem 3/10 not 7/20 but other than that this video was a big help thank you, cram night lol
thanks a lot bro
Nice. Thanks
At the point where you have x/((x^2)+1) can that intergral be taken as arctan(x)?
how can i solve the double integration of xy^3/x^2+1 where 0
Thanks man
Wow this taught me more than my math lecturer did in 2 hours.
I did this exact problem today in class, the final answer is actually 3/10 (when you adjust for the mistake in the video, which PatrickJMT has pointed out for us in the video).
@KingOfShadows92, in the outer most integrals, the limits of integration MUST be constants. The limits of integration in the inner integral can contain only 1 variable . And when doing triple integrals, the inner-most integral can have limits of integration that contain at most two variables. Correct me if I am wrong I need to be sure for my test.
I can't understand why are the x limits as such
do you have any graphs for triangular regions or say a rectangular region with x+y
Great video. Does the double integral of F over a region have a physical interpretation? Thanks.
@odoc01 He didn't have to plug it back into the original variable because by changing the limits he changed the integral. If he had kept the same limits then he would have had to switch the variable back. Good luck on your midterm!
in the first one, why did you not multiply the fraction by y if we are treating it as a constant?
Yeah, I think he made a mistake there
Great Video! I have a quick question patrickJMT ,
does it matter whether we integrate it as a type 1 region or type 2 region? Like does it matter if we draw the "arrow" up to down and then integrate using those equations as opposed to if we draw the "arrow" left to right and integrate using those equations... ? I've noticed I get different answers some of the times.
Both methods will give you the same answer if done correctly. Good luck!
There are some functions where only one way works.
There is a reason why you change the order of integration, meaning sometimes you can only work with either one of those.
The answer to the second example should've been 3/10. The mistake happened around 8:42 when you wrote "x^4 / 4" when it should have been x^4 / 2.
Is it always the case that after we execute the 2nd integration, our answer should be a constant? And should the outer bounds of integration should be constants?
@Tkdkid9 ok! many of the comments point out the mistake i do believe
When you're substituting U into the integral, you're basically integrating U as a variable. If the original limits of integration were let's say 0 to 1 for X, then when you're substituting X as some function of U ( u=x+1 or something), then obviously your limits have to change as well, since your variable is not just X anymore.
Final problem should be 3/10.
Finally, I knew it. Exactly, because he should of gotten (x^2)2/2 = x^4/2 and not x^4/4. Then when integrated, you should get x^5/5•2 = x^5/10. At the end it should be 4/10-1/10 = 3/10 and NOT 7/20.
Good thing I look at the YT comments after problems, just to clarify his mistakes.
I meant to say (x^2)^2/2. ***
No worries, dude; always double check work. Both insanely smart professors and elite textbooks make mistakes sometimes so always ask questions and check what people are saying.
+Cam Staubus yes 3/10 is correct
gee, ur great!... keep it up!...
When u initially begin the integration of 2/(x^2+1) do you not treat that as a constant and multiply that times y?
4:00 Don't you need to multiply the (2/x^2+1) by y? because isn't that how double integrals work..? ugh i am confused
thanks!! help a lot!! :-D
@TokeItUpTyler well, tell that to the person in one of the other videos that was bitching cause i derived something. his comment: this is a useless waste of time, we can just memorize the formula. who cares about deriving?
and i think most teachers do try to explain things the best they can. often times students do not ask questions so the teacher is left to guess whether or not they are getting through.
on the first question: no need to put the values of U back? which is x^2+1 ?? by the way after 10 years but still helpful God bless...
do u always integrate (inner int) with respect to y first?? and do the notations always have to be dydx or can it be dxdy, or is dydx just used more because its easier??
Why didn't you add y to 2/(x^2+1) term in 3:55 like you did to the x term in 7:58?