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
@JuliaPaler3 жыл бұрын
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!!
@kristakingmath3 жыл бұрын
Awww thank you so much, Julia! Congrats on working through your Bachelor's... that's awesome! :D
@Gmaraio72339 жыл бұрын
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?????
@kristakingmath9 жыл бұрын
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!
@kristakingmath11 жыл бұрын
yes! planning to add line integral videos. :) so glad you liked this one! :)
@kikwangk47938 жыл бұрын
upcoming calculus finals next week.. you're videos really help me Krista thank you so much!!! love you
@kristakingmath8 жыл бұрын
I'm so glad I can help along the way! Best of luck next week... you got this!
@kristakingmath11 жыл бұрын
i'll definitely be adding more as part of my foundation for calculus. i'm so glad you like my videos!! :D
@23alexpb11 жыл бұрын
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!
@sunzheyuan1117 жыл бұрын
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 KZbin videos!!
@kristakingmath7 жыл бұрын
That's so exciting! Best of luck to you! :) I'm glad the videos have been able to help along the way.
@justinaseptember57099 жыл бұрын
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!
@juliawebster71347 жыл бұрын
I almost cried! Ive been trying to find this example explained forever.
@kristakingmath7 жыл бұрын
Aw I'm so glad you found it! :D
@hg2.7 жыл бұрын
Best math teacher on KZbin.
@ericsmidt69233 жыл бұрын
Wanted to tell you how great material you have here! Thank you!
@kristakingmath3 жыл бұрын
You're welcome, Eric, I'm so glad you're enjoying it! :)
@xXBR4D3NXx7 жыл бұрын
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.
@lautyx185 жыл бұрын
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 )
@billyram99911 жыл бұрын
Keep up the good work! You have the tidiest, cleanest and most informative tutorials out there!
@kristakingmath11 жыл бұрын
Glad you liked it! :D
@kristakingmath11 жыл бұрын
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! :)
@momo_drum11727 жыл бұрын
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
@kristakingmath7 жыл бұрын
I'm glad you like them! :)
@shinkoihime385011 жыл бұрын
you are better than my teacher. thanks Krista.
@panchogeorocks8 жыл бұрын
PERFECT! Very Thoroughly explained! Great vids Krista :)
@kristakingmath8 жыл бұрын
Thank you so much! :)
@AhmadRaza-fi3xo4 жыл бұрын
Great video Krista ! helps a lot.. keep up the good work .. Thanks
@kristakingmath4 жыл бұрын
Thanks, Ahmad! Glad it was helpful! :)
@Mjorh11 жыл бұрын
Thanks! Comprehensive n simple , So better than teachers! Keep up the great work !
@AnotherPCAddict8 жыл бұрын
I love you. Honestly. Seriously. You're the best. Seriously. Thank you!
@kristakingmath8 жыл бұрын
+AnotherPCAddict You're welcome, I'm so glad you like the videos!
@kristakingmath11 жыл бұрын
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.
@Geffosome10 жыл бұрын
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
@Neueregel11 жыл бұрын
Very nice tutorial ! These doubles are very useful in Vector Calculus
@kristakingmath11 жыл бұрын
yes they are! i'm glad you like it!! :D
@dzmitryk96582 жыл бұрын
So awesome! Thank you!
@kristakingmath2 жыл бұрын
You're welcome, Dzmitry! :)
@kristakingmath11 жыл бұрын
Awesome!! I'm so glad you're starting to enjoy calculus, and I really hope it helps you with your research! :D
@MisterBinx8 жыл бұрын
Man I need to brush up on u substitution and probably also integration by parts. I wish I would have practiced that more.
@hg2.7 жыл бұрын
Right, "who doesn't need to brush up on u substitution. " Luckily you've got Krista to basically brush it up for you. (!)
@kristakingmath11 жыл бұрын
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! :)
@kristakingmath11 жыл бұрын
You get a sneak peak from my website first. ;)
@Coffeehandle8 жыл бұрын
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?
@kristakingmath8 жыл бұрын
+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!
@Coffeehandle8 жыл бұрын
Ah I see. Your method here seems more logical and more simple. Appreciate the help, as always!
@SunnySharma-ip1xn11 жыл бұрын
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
@kristakingmath11 жыл бұрын
you're welcome! i really hope you like it!! :D
@electronicjunky69407 жыл бұрын
very helpful. thanks!
@kristakingmath7 жыл бұрын
Glad it could help!
@TheMath27006 жыл бұрын
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?
@kristakingmath6 жыл бұрын
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)).
@Abhiabhiabhi97abhi7 жыл бұрын
Awesome video! It helped me a lot! You're a saviour really, Krista! :-)
@kristakingmath7 жыл бұрын
Thanks! I'm glad the video could help. :)
@jeffreysimanjuangwescott214610 жыл бұрын
Thanks, that's very helpful.
@kristakingmath11 жыл бұрын
Thanks!
@kristakingmath11 жыл бұрын
That's such a nice compliment, thank you! :D
@gokhankelebek11 жыл бұрын
Nice video, i wish you a great audience. By the way which software do you use for your lectures?
@kristakingmath11 жыл бұрын
I explain the process here :) integralcalc . com/how-I-create-my-videos
@kaustavphukan395111 жыл бұрын
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.
@MrMoeqt11 жыл бұрын
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?
@MrYusufgovani11 жыл бұрын
As usual excellent explanation. Thank you for making great videos! Yusuf
@user-he4dk4sb7h11 жыл бұрын
I loved the video!! It is awesome!! Planning to do something on the contour integral (line integral)? Thanks!!
@infosecgaurd72048 жыл бұрын
Actually where did that 1/2 go after you substituted u for x^2+1 and cut it?
@kristakingmath11 жыл бұрын
I'm glad you like my style! :)
@Pwntatoz7 жыл бұрын
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?
@cliffordwilliams4739 жыл бұрын
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?
@kristakingmath9 жыл бұрын
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.
@JFelipePV11 жыл бұрын
Can it be integrated like dx dy instead of dy dx whats the difference
@kristakingmath11 жыл бұрын
Thanks Yusuf! :D
@BBP8549 жыл бұрын
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.
@kristakingmath11 жыл бұрын
you're not stupid! :D i should have explained it better, but i'm glad it makes more sense now! :)
@moonhunter66657 жыл бұрын
Hey nice videos! Don't suppose you got any on those integral theorems(like Stokes's/Divergence theorem etc.)? Otherwise good job :)
@@kristakingmath you did a great job. I appreciate that . You are the best 😁
@kristakingmath10 жыл бұрын
you too! :)
@ghanousaoud92597 жыл бұрын
tnx madam
@isaacmabitsela68643 жыл бұрын
My professor just clicked the unlike button. he thought i was dumb i cant pass math until i saw this videos
@RileyEscobar36611 жыл бұрын
Why are these Multiple Integral videos unlisted?
@ghanshyambharate21306 жыл бұрын
i think you started to imagine maths like a scientist that's pretty awesome for girl.
@badraig8009 жыл бұрын
how about if I flip Dx and Dy
@masso1729 жыл бұрын
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.
@kristakingmath11 жыл бұрын
i don't! i have to always keep reviewing. :)
@techgoldtreasury96478 жыл бұрын
thanks mam
@kristakingmath8 жыл бұрын
You're welcome!
@techgoldtreasury96478 жыл бұрын
thank you very much
@Nalber310 жыл бұрын
you're awesome
@gaetanodagostino71278 жыл бұрын
This is the most simple case of double integration and you explained in such a complicate manner. lmao
@SunnySharma-ip1xn11 жыл бұрын
How do you m
@flawns10 жыл бұрын
BUT why dy then dx???
@flawns8 жыл бұрын
Rick Freeman Thanks for the reply! Went to professors office and they explained it. Already finish Ordinary Differential Equations
@malekdawed89928 жыл бұрын
i dont know your name but thanks for this explected my teacher
@kristakingmath8 жыл бұрын
+MALEK DAWED My name is Krista, and you're welcome!
@kristakingmath11 жыл бұрын
i'd be happy to byron... consider us related. ;)
@MrMoeqt11 жыл бұрын
Ahhh, I see! Sorry for my stupidity, thanks anyway I get it.
@ReussieBaez11 жыл бұрын
Une professeure tres jolie, je voudrais avoir quelqu'une comme toi :D
@ryangifford31729 жыл бұрын
will you marry me?!
@Porty11199 жыл бұрын
I'd probably say the same were I not in an amazing relationship right now...this gal is crazy helpful!