Double integrals (KristaKingMath)
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- čas přidán 15. 06. 2024
- ► My Multiple Integrals course: www.kristakingmath.com/multip...
Learn how to find the double integral of a function, which represents the volume which sits on top of some region, often a rectangular region, but below the given function.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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I don't know about marriage yet, since we don't know each other, but I promise to keep the videos coming! I'm glad you like them!! :D
I remember when I first found you in high school when I was taking Calculus, and now I'm in my second year of university working on my Bachelor's degree in engineering and I still watch you! Thank you so much for such high-quality videos!!
Awww thank you so much, Julia! Congrats on working through your Bachelor's... that's awesome! :D
yes! planning to add line integral videos. :) so glad you liked this one! :)
Seriously how are you so smart....you go from teaching how to add fractions to this ....unbelievable. How did you get so good and qualified at math?????
Gmaraio7233 That's nice of you to say! I tutored for many years before, and that's how I got started making videos. I hope they're helping!
Keep up the good work! You have the tidiest, cleanest and most informative tutorials out there!
i'll definitely be adding more as part of my foundation for calculus. i'm so glad you like my videos!! :D
Thanks!
Comprehensive n simple , So better than teachers!
Keep up the great work !
Glad you liked it! :D
upcoming calculus finals next week.. you're videos really help me Krista thank you so much!!! love you
I'm so glad I can help along the way! Best of luck next week... you got this!
Wanted to tell you how great material you have here! Thank you!
You're welcome, Eric, I'm so glad you're enjoying it! :)
PERFECT! Very Thoroughly explained! Great vids Krista :)
Thank you so much! :)
Very nice tutorial ! These doubles are very useful in Vector Calculus
Great video Krista ! helps a lot.. keep up the good work .. Thanks
Thanks, Ahmad! Glad it was helpful! :)
I love you. Honestly. Seriously. You're the best. Seriously. Thank you!
+AnotherPCAddict You're welcome, I'm so glad you like the videos!
Hi Teacher, I´m a biology and Phd student in Brazil and I´ll spend little time in USA carrying out the research. I´m developing mathematical models to study cancer dynamic population. I havent studied Calculus before but you introduced a math passion in my brain! Well hope you got a new fan and student. Hugs from Brazil!
Thanks, that's very helpful.
you are better than my teacher. thanks Krista.
Awesome!! I'm so glad you're starting to enjoy calculus, and I really hope it helps you with your research! :D
I explain the process here :) integralcalc . com/how-I-create-my-videos
As usual excellent explanation. Thank you for making great videos!
Yusuf
So awesome! Thank you!
You're welcome, Dzmitry! :)
you can absolutely do it either way, you just need to make sure that you switch your limits of integration if you switch your order of integration. you want to integrate in the order that makes the problem easiest to do. sometimes integrating in a certain order is MUCH easier than the opposite order. which means, if you're having a hard solving an integral, try flipping the order and see if that makes it easier! :)
Aww thanks! I'm so glad you like my channel. As for the videos, practice helps. :) I had the same troubles in my early videos.
I almost cried! Ive been trying to find this example explained forever.
Aw I'm so glad you found it! :D
Best math teacher on CZcams.
Your videos are the best. I rely on them to help me understand things quicker without a headache! Thank you so much. You're like a lady Feynman
I'm glad you like them! :)
Very helpful, thank you ^^
yes they are! i'm glad you like it!! :D
I loved the video!! It is awesome!! Planning to do something on the contour integral (line integral)? Thanks!!
Awesome video! It helped me a lot! You're a saviour really, Krista! :-)
Thanks! I'm glad the video could help. :)
Sometimes it's easier to change the limits of integration and not switch back, sometimes it isn't. When I worked out this problem I did change them.
very helpful. thanks!
Glad it could help!
I am going to do my calculus and linear algebra exam in 5 days. If I pass this exam, I will not have any math course anymore. Thanks for your explicit and clear lectures!! I will recommend my friends to watch your CZcams videos!!
That's so exciting! Best of luck to you! :) I'm glad the videos have been able to help along the way.
Thanks!
I love your videos, I am gonna be in algebra 2 but i discovered your videos and they are very intriguing, I hope you make precalc videos in the future please it will benefit mankind
That's such a nice compliment, thank you! :D
Nice video, i wish you a great audience. By the way which software do you use for your lectures?
you're welcome! i really hope you like it!! :D
Think about x/(x^2+1) as something else, like an apple. We have 27/3 apples plus 27/3 apples, which means we have 54/3 apples. Kind of a silly analogy, but the 27/3 is just a coefficient on those identical terms, so you add them together. Or just think about x/(x^2+1) as A. You've got (27/3)A+(27/3)A, so you get (54/3)A. Hope that makes more sense! :)
That part when she calculates y. You can write in easier way, the way at least I understand very well. (1/3 x/x^2+1 ( 27 - (-27) ) ). I mean you don't need to write this '1/3 x/x^2+1' two times, simply put this whole thing into brackets, like you would do: (A(27+27)) same as 27A + 27A.
And by the way, I really appreciate your tutorials. They helped me A LOT. THANK YOU!
You get a sneak peak from my website first. ;)
Man I need to brush up on u substitution and probably also integration by parts. I wish I would have practiced that more.
Right, "who doesn't need to brush up on u substitution. " Luckily you've got Krista to basically brush it up for you. (!)
Hey nice videos! Don't suppose you got any on those integral theorems(like Stokes's/Divergence theorem etc.)? Otherwise good job :)
one way to make integration with u substitution easier is to change the boundaries so if u is x^2+1 then the limits would be from 1 to 2 instead of 0 to 1 because for me personally i forget to substitute the original x equation back in the place of u so i just evaluate with u at the old boundaries so you can substitute x for u and change the limits of integration from 0 and 1 to u(0)=1 to u(1)-2
At 5:05, why is is it 54/3 x/x*2+1 instead of 54/3 2x/2x^2+2 , I thought that was what 2(54/3 x/x*2+1) was. Because you are adding them together right? Just how you add the twenty seven to the other twenty seven?
Actually where did that 1/2 go after you substituted u for x^2+1 and cut it?
Thank you for making such nice videos. Helping me a lot in school. By the way,you have a lovely voice and a pretty face.
Can it be integrated like dx dy instead of dy dx whats the difference
I'm glad you like my style! :)
Nice and lovely presentor
Thanks Yusuf! :D
Is it a legitimate method to just separate the limits and terms and say: integral (x/x^2+1)dx * integral (y^2)dy using their respective limits? I get the same answer here, but I'm not sure if it always works.
Was there a reason to why you chose that order (dydx)? Could you have done it with dxdy and changing the order of the integrals?
You might have been able to flip the order of integration (you can for most integrals), but for this particular integral, integrating with respect to y first is easier. That's because you can factor out the (x/(x^2+1)) as a constant coefficient and you really only have to integrate y^2 to get (1/3)y^3. But if you do it the other way and integrate first with respect to x, you can only factor out the y^2 as a constant coefficient, and then you have to integrate (x/(x^2+1)).
sweet!
How do you remeber all these topics?
thank you so much
You're welcome, ossama! :)
@@kristakingmath you did a great job. I appreciate that . You are the best 😁
My professor taught me that when ever you do u-sub, you also have to change your limits of integration using the x and u relationship. In this video for instance u-x^2=1. So you would plug in your x values of integration and solve for u. Those values would be your new limits of integration.
Is this the proper way to do it? Or do you come to the same answer with either method?
+David Alderman You have two options, both of which will arrive at the same, correct answer, assuming you do everything correctly. 1. Like your professor said, change the limits of integration so that they're in terms of u when you make the u-substitution. Once you integrate, you can evaluate directly over the new interval. 2. Like I did here, leave the limits of integration in terms of x when you make the u-substitution. Once you integrate, you'll have to back-substitute to put the problem back in terms of x, and then you can evaluate over the original interval. Hope that helps!
Ah I see. Your method here seems more logical and more simple. Appreciate the help, as always!
Why not just push out the 1/3 constant and the temporarily constant X Function so you don't have to fuss with it while you take the integral of y?
why didn't you change limit of integration?
what programms do you use to create your videos?
www.kristakingmath.com/blog/how-i-create-my-videos :)
tnx madam
Why are these Multiple Integral videos unlisted?
Thanks
+Anas Kodematee You're welcome!
Just to clarify, I noticed you didn't changed your limits of integration when using U-substitution. Why is that and in when would you have to change your limits of integration?
Clifford Williams I didn't change them because I knew I was going to back-substitute at the end. If you're not going to back-substitute, then you need to change them.
you too! :)
you're not stupid! :D i should have explained it better, but i'm glad it makes more sense now! :)
you're awesome
Great vídeo as always!. One little trick that may be of interest:
Integral of [f'(x) / f(x)] = ln | f(x) |
In other words, if you have to integrate a function where the numerator is the derivative of the denominator, the result of this integral is the natural logarythm of the absolut value of the denominator. It can save you some time if you notice. In this case you wouldn't need to use u substitution for the x integral ( 5:10 )
how about if I flip Dx and Dy
Just flip your bounds to match dy dx and you can still solve. Sometimes you have to choose your bounds depending on what would be easier to integrate at the end. I try to leave the bounds with no variables on the outside of the double integral.
How do you m
thanks mam
You're welcome!
thank you very much
i think you started to imagine maths like a scientist that's pretty awesome for girl.
i don't! i have to always keep reviewing. :)
My professor just clicked the unlike button.
he thought i was dumb i cant pass math until i saw this videos
BUT why dy then dx???
Rick Freeman Thanks for the reply! Went to professors office and they explained it. Already finish Ordinary Differential Equations
This is the most simple case of double integration and you explained in such a complicate manner. lmao
i'd be happy to byron... consider us related. ;)
i dont know your name but thanks for this explected my teacher
+MALEK DAWED My name is Krista, and you're welcome!
Ahhh, I see! Sorry for my stupidity, thanks anyway I get it.
Une professeure tres jolie, je voudrais avoir quelqu'une comme toi :D
xD
will you marry me?!
I'd probably say the same were I not in an amazing relationship right now...this gal is crazy helpful!
:) #hugs
you are so beautiful!!!!!!!!!!
Now tell me about yourself
Nice and lovely presentor