You are an ANGEL sent from MATHS HEAVEN to help us poor souls to see the MATH LIGHT- AND what a brilliant job you are doing- thank you from one of your many disciples....
I like that you delved more into the concept and visual/geometric interpretation of a double integral. This was a wonderful, conceptual video, and I wish you did the same thing for all your other ones. Well done!
You earned my like the moment you drew the stick figure looking at the rectangles. Little details like that are so helpful in understanding these concepts. Thank you for explaining so well!
Glad that I watched this video. I took calculus some 28 years ago and only recall the basic concepts of limit and Riemann sums. So amazing that such a simple concept is so POWERFUL
If we had many Kristas around the world who approaches math concepts in the manner you do, surely many students would find Math enjoyable and fun. Excellent work Krista and thank you for sharing such an important piece of work!
This is fantastic. Now I know where n and m come from and also R and A. Many many thanks. I have a much greater understanding this topic. I can't thank you enough
10X a lot! This made it completely clear for me. I didn't even know that double integral represented a volume, I guessed it'd represent an intersected area between two functions, one of them is Y(x) and the second is X(y).! Keep it up🤞
I love the way you present! Your "SIMPLICITY" ways with your golden and sweet voice makes it lovely and interesting! Your explanations are more crucial and impressive than a full day stupid lecturer. Thank you Krista again and again for devotion and dedication! So are sweet in and out! Cause you make the bitter and difficult part sweet! That flows in a lovely manner!
Great Video Krista! I wish you would have mentioned that da = dxdy just to show how the dx and the da relate. Could you do a video on what triple or more integrals represent? I have always been confused what those meant since a double was already volume. Thanks!
You are right I got straight A's in calculous, and now am doing rewiews, the integretion process is easy for me, but still hanve trouble visualizing double and tripple boundaries!!!
It's really Wonderful video😀... Put some more video like this about fundamental I loved it 😍 There are so many excellent and wonderful teachers here in India but the problem is that all are not on social media or TH-cam.
A very cogently presented video. But I would like to know, just as in the case of a velocity-time graph, the area under the curve represents the distance travelled, what various things could the volumes under surfaces given by double integrals represent? Thanks once again for the excellent video.
Hello again! I'm excited for the new school year! I'll be posting again regularly, starting this week, with how to interpret a double integral. :)
Krista King good job 👏🏻 😘
Thanks!
thank you for this, my calc 3 class is taking off from here, so this is super useful
Krista King nice topi plz express triple intrigal
Awesome, I'm so glad! Good luck in Calc 3 this semester! :D
You are an ANGEL sent from MATHS HEAVEN to help us poor souls to see the MATH LIGHT- AND what a brilliant job you are doing- thank you from one of your many disciples....
I like that you delved more into the concept and visual/geometric interpretation of a double integral. This was a wonderful, conceptual video, and I wish you did the same thing for all your other ones. Well done!
You are the best. You make everything so easy to understand and yet preserve the beauty of the subject matter.
😊
You earned my like the moment you drew the stick figure looking at the rectangles. Little details like that are so helpful in understanding these concepts. Thank you for explaining so well!
I'm so glad it helped!! :D
Glad that I watched this video. I took calculus some 28 years ago and only recall the basic concepts of limit and Riemann sums. So amazing that such a simple concept is so POWERFUL
If we had many Kristas around the world who approaches math concepts in the manner you do, surely many students would find Math enjoyable and fun. Excellent work Krista and thank you for sharing such an important piece of work!
One of my NEW fav channels! Thank u!
Best explanation on yt by far... Great job Krista!
You've opened my eyes, literally. Thank you Krista :)
Your clear pedagogy makes us love math. Many thanks
This is the best explanation of an integral I have seen on TH-cam
Great understanding+great concepts+great explaination+calm voice=great video.
Amazing work, i understood every single detail :)
Awesome!! :D
i cant believe how awesome this is, so clearly and simply explained. very nice!
Best presentation I've seen. Simple enough and very understandable. Keep up the great work!
😊
Now this is what I was looking for. Feeling short of words to express my gratitude towards you. Excellent video!!!
I know a million people have probably thanked you since you posted this video but, I needed to thank you because this helped a lot! Thank you!
You're welcome, Brandon, I'm so glad this helped!! :D
subscribed as soon as I heard your sweet voice, very well explained, you are an amazing teacher
Thank you so much, Blackfyre, I appreciate the sub! :D
Best overview in double integrals ever! And your voice is so soothing.
Thanks, Erika! So glad you liked the video. :)
Not only did this explain Double integrals perfectly, it also summarized single variable integrals very nicely. Wish I had found your videos earlier!
Why this video is so underrated. Never see an explaination before. Thank you
I'm so glad you liked it! :)
Thank you so much Krista, your videos are great and so helpful. You were born for this
This video gives you a good intuitive grasp of double integrals! Thamk you!
Thank you, Krista, the explanation has a good stepping-difficulty. And colour-code is awesome too!
Please come back Krista I need you to be my Calc 3 professor
Can't thank you enough! You are an amazing teacher!!! Kudos to you! 😊
Thank you so much, Ketki! :D
Beautifully Explained...! Thank you for the detailed illustration of double integral.
You're welcome, Saurabh, I'm so glad you enjoyed it!
wow! I was not understanding the significance at all but ur pictoral explanations clear all my doubts.Thank u so much
Hi Krista, this is a beautifully sustained 25 minutes (and a bit) of clear exposition. Thank you!
Your explanation is very simple and precise.Thank you for your lesson 😍😍
You're welcome, I'm glad you liked it! :D
Crystal clear amazing video. Very detailed.
This is fantastic. Now I know where n and m come from and also R and A. Many many thanks. I have a much greater understanding this topic. I can't thank you enough
You're very welcome, joliet, I'm so glad this helped clarify! :D
Awesome.....now it makes sense why i should study more about them and i will.....thanks krista🖐️🖐️🖐️
I like it very much, It was very difficult to me to understand by the books, but your video just simplify everything, thank you!
You're welcome, I'm so glad it helped!! :D
Thanks Krista! This was another great video.
10X a lot!
This made it completely clear for me.
I didn't even know that double integral represented a volume, I guessed it'd represent an intersected area between two functions, one of them is Y(x) and the second is X(y).!
Keep it up🤞
So glad it helped, Ahmad!
You are an amazing teacher, thank you!
Thank you so much, Carlos! :D
very well done.
+1 for sure.
Thank you so much! :)
what a brilliant way to teach, please keep going
I will, thank you so much! :D
Thank you Krista!
You're welcome, Sofia, thank you for watching! :D
I AM A 0 PERSON IN MATH, BUT YOUR EASY EXPLANATION ENTERTAIN ME REALLY AND TEMPT ME TO DELVE INTO MATH. THANK YOU MY BELOVED SISTER TEACHER. Arun dey
If this lady had been my math teacher, I'd be a mathematician today.
Simply superb...Awesome...Please upload this kind of videos more ... It will be so much helpful to Mathematics lovers...Thank you so much madam...
you are a savior. Bow down to the math goddess 🙇♂🙇♂
I love your videos Krista!
You are great.
Your videos have been helping me since I was studying Calc I.
Wow, awesome! I'm so honored, thank you so much for your support! :D
You made it easy for me. thanks KRISTA .
Nice explaination.
I got cleared my concept,thru urr video.
Thanx a lot.
You're welcome, Shivam, I'm so glad the video cleared things up! :)
*Thx Krista King for this vid; your explanation is pellucid and you are indeed erudite in mathematics.*
Thank you, Ivor! :D
You have a beautiful voice, thanks for the video 😊
❤thanks a bunch
I just say that I love you . Excellent ob .1st time some 1 clear the most difficult concept.
Awesome.. Beautiful lecture!!
Awesome
I was stuck on this topic for like a week
Thank you 😊
You're welcome, Harsh! I'm happy to help! :)
I love the way you present!
Your "SIMPLICITY" ways with your golden and sweet voice makes it lovely and interesting!
Your explanations are more crucial and impressive than a full day stupid lecturer.
Thank you Krista again and again for devotion and dedication!
So are sweet in and out!
Cause you make the bitter and difficult part sweet!
That flows in a lovely manner!
Thank you Krista...I was wracking my head.. .it was a great relief!
You're welcome, I'm so glad it helped!! :D
Thanks for the nice illustration!. Could you please share which tablet are you using here & which white board software?
Good video! What software/tool do you use to draw the diagrams for this video if you don't mind?
It's called Sketchbook. :)
Brilliant work.
Thanks, Anup!
Good craic. Looking forward to the next one.
Thanks, Piper! :D
Aye Cheers! While I've got your ear, integration in other coordinate systems would be a great topic. =)
Great Video Krista! I wish you would have mentioned that da = dxdy just to show how the dx and the da relate. Could you do a video on what triple or more integrals represent? I have always been confused what those meant since a double was already volume. Thanks!
I'll try to make one! And great point about the dA=dy dx... I appreciate the feedback! :D
I love your math lessons
Nice work!!!! Thank you!!!!
Thank you so much! :)
Krista king and organic chemistry tutor are the best calculus teachers in the world ❤❤❤
thanks , now i really understood what is mean by double integration.
The way you explained was Extra-Ordinary !! ,Thanks for helping in understanding the double integral !!!.
You are right I got straight A's in calculous, and now am doing rewiews, the integretion process is easy for me, but still hanve trouble visualizing double and tripple boundaries!!!
Outstanding!!
Thank you very very very much, I understand this perfectly.
You're welcome, I'm so glad it helped! :)
Thank you so much, Krista. I now have a different perspective towards multi-variable calculus.
You're welcome, Dev! I'm so glad you liked it! :)
very satisfying video.thank you
Thanks, Vishal, so glad you liked it! :D
Thanku mam, i never find such a nice explaination of double integral, once again thanku
Thanks, Pradeep! I'm so glad you liked it! :D
It's really Wonderful video😀...
Put some more video like this about fundamental I loved it 😍
There are so many excellent and wonderful teachers here in India but the problem is that all are not on social media or TH-cam.
I'm glad you liked it, I'll definitely be making more videos! :D
Is this video on your website?
Very detail but concise at the same time. Would live to be your student.
A very cogently presented video. But I would like to know, just as in the case of a velocity-time graph, the area under the curve represents the distance travelled, what various things could the volumes under surfaces given by double integrals represent? Thanks once again for the excellent video.
Thanks from France !
Fantastic video btw
very nice video
Gracefully made
Thanks, Daniel!
Thanks you mum........ Love you... God bless you
Soooo sooo thanks for this perfect video
that's fantastic - now what applications would that have in the real world other than finding the volume as you have demonstrated.
I'm so grateful 🙏🏻🌷🌷
sheesh, amazing work
Very good video !
Thanks you :)
I was supposed to see this on this semester but my professor decided to leave it out of the program. So thank you! This will be useful.
You're welcome, I'm happy to help! :)
thank you 🥰
You're welcome! :)
Yeah.. Its really helpful.. Video is quite bit little lenthy but a very nice explanation has been given... Its very helpful for me..
thank a lot...
plz solve my dout
by single integration we get area then by double integration do we get volume than what by triple integration
Great video really
Thanks, Ahmed! I really appreciate it! :)
You are indeed Krista King!
Hi Krista, you're awesome.
Krista is really good in maths, does any know whats her academic background in maths ?
Wow very nyc explained mam thanks
Now, THIS, is how you introduce a subject; just wow.
how to hit the DOUBLE like?
Thanks u for making such a great video!! :)))
You're welcome, I'm so glad you liked it!
Thank you somuch Mam..A great job
Mam,The method of teaching is highly impressive.I would like to know the technical packup
Thank you, Anie, I'm so glad you liked it! :)