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Expressing a triple iterated integral 6 ways (KristaKingMath)
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- เผยแพร่เมื่อ 5 เม.ย. 2014
- ► My Multiple Integrals course: www.kristaking...
Learn how to change the limits of integration and order of integration to express a triple iterated integral in 6 different ways.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
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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.kristakingm...
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at 6:00 I think x^2 = 4 gives x = + or - 2 instead of sqrt of 2
correct
Thank you soo much test tomorrow and no clue how to even start these !! lol
oh and bit confused @ 5:47 shouldn't x = +/- 2 not +/- (2)^(1/2) ? a
I've never been told a methodical way of doing triple integrals like this. You've saved my life.
+Laura Gibbs I'm so glad it helped!
I only discovered your channel this weekend as I'm reviewing for my final - this is the most helpful, clear, incredible perspective on math that I've ever seen. Now I'm really considering subscribing to your website for my differential equations course next semester. I wish I had known about your work before I started college.
Your chart method is such an intuitive way of looking at things. Thank you Krista, this really helped!!
This is more efficient and reliable than the methods they teach us, not to mention easier to understand.
Could you do a problem where the bounds of the original integral are given and then find the new integrals by graphing the bounds? I have trouble on how to slice the region.
dude your a living legend! this is like the 30th video ive watched from you on multi variable calculus!
sqrt4 does not equal root2..
Brandon Jones yeah i was like what is she smoking
dude yeah she made a mistake unfortunately
@@user-sx5kx3pq2i She was teaching in a so nice approach. She did it so correctly. Unfortunately if she made one mistake, u shouldn't comment like this. After searching so many videos i found it more clear and transparent.
@@user-sx5kx3pq2i NSJSJJSJSJSJ
watching this 2 hours before my exam.....
I hope your exam went great!
watching 10 minutes before exam
@@ghubb watching during the exam
@@emirmazlum8339 Watching after exam :/
I just have to say thank you - thank you so much! Neither my textbook or online homework explained how to come up with the limits, which I think is the hardest step of evaluating the integral. This is genius!!!!!
I watched too many different videos and most of the people can not explain this order of integration very well. you made it so simple and help me too much. thank you very much.
You're welcome, Muhammad! I'm so glad it helped! :D
This is a godsend for those of us who suck at graphing and visualising. This is the only thing I've seen that actually makes sense at all.
I'm so glad it helped, Thoran! :D
Hi Krista, the constant values for x should be 2 and negative 2 instead of positive and negative root 2.
Wow! The table is a stroke of genius. Thank you kindly for helping us make heads from tails or some kind of Cartesian equivalent :0)
+John Gonsalves You're welcome, I'm really glad it helped!!
THANK YOU SO MUCH! My teacher didn't explain this well, and I was so grateful for this video, especially when you introduced the table! Thanks again, Krista!
You're welcome Emily! Glad it could help. :)
This is a topic I have been struggling to Understand in Multivariate calculus for a long time now and you have made things very clear for me with this video!
+ethan glenn I'm so glad I could help!
Krista is the goat, saved me fr
That was the best possible explanation on how to do these. You're awesome.! Thank you very much Krista!
Aw thanks! Glad you liked it!
thanks for perfect explanation.I have taken this course 3 years . Now , I ' m clear
I'm glad it could help!
Our lecturers can’t explain like this 🥺.Thank you so much 🔥🔥🔥🔥
You're very welcome, Privilege! I'm happy to help! :)
should that be root of 2 or just 2??
You are a lifesaver!
how do you use this method if you are only given the limits of integration
great lesson... is there a way to do it 9 ways with a solid bounded above z=x+y-2 and below z=0? I know how to do 6 from your lesson, is there 3 more ways... I was thinking of splitting the solid in 2 and triple iterate the integral with half the solid... I know I am looking at an isosceles triangle, if I am looking above the solid.
What if you are given the limits of integration instead?
Thumbs up Ms. you've really helped me...thank you!
It cleared my doubt. Thanks a lot 🙏💕 from 🇮🇳
Fantastic... I am to much worried about this topic. But after watching this video I am able to solve such kind of problem 😊😊🙂... Thank you ❤️
+/-2
I had to subscribe after watching. The limits of integration can be tricky but, you break it down..
Please keep making videos like this to help everyone with calculus🙏🙏
😊
watching this 2 hours before my exam lmao
Watching this the day before my test, thank you!! :)
You're welcome, Danika! I hope the test went great! :D
A soul less tour de force. Ought to explain at the outset thar 1) first we write an equation of one side expressed in terms of the other 2 sides.
2) we then integrate this equation (of the first side) over the next side to get an area and express them in terms of the 3rd side.
3)Finally we integrate this area over the 3rd side between definite limits to get a definite integral representing a numerical volume.
BEST TIP EVER
I have a similar question
A solid in the first octant containing the origin and bounded by sections of the plane y = 1 + 2x and
the sphere x^2 + y^2 + z^2 = 4
How can we expres in 6 ways?
It seems that i cant use your method...
Thank you.
Try intersecting both equations you have and then using the 3 equations you have! That third equation must be what you're missing!
thank you, these originally just looked like a puzzle or something to me until I saw how to do them systemically
You're welcome, Cinemá! :D
Quick question: Does this work for any triple integral? I'm really bad at sketching and visualizing domains in 3 dimension. If so, this would be a godsend.
I'm so glad I saw this
Though this video is very useful, this method can be applied only when its possible to form such a table. But look at this question : Find the volume under the surface x+2y+z=4 and above the circle (x^2)+(y^2)=4 in the xy plane. It's not possible to form the table in this case. Thank you as it has helped me to solve questions where I can form the table of limits.
Spectacular explanation
Thank you so much, Nikhil! :)
Thanks. I've always wondered what to do with these "general" problems in which no or few limits of integration are given. Do you have a vid that covers how to pick the best order, or is this something only gained by experience?
this never made so much sense!!! calc 3 exam tomorrow! thank you
You're welcome, hope the exam went great!
Thank you so much!
Does this always work?
how can we thank you enough for your great help?
your voice is so calming
Terrific video plus the Jacobian one. Thanks.
Thanks, Rajendra! :)
This is so helpful. Thank you for making this video.
+Will Alex You're welcome, I'm so glad I could help!
Nice madam
The steps are quite good.
The steps you taught ....is very good.
Thanks a lot, Bapuna! 😊
Thank you, Krista!
You're welcome, Zephyr!
My teacher didn't teach this.... thank you so much
You're welcome, Spencer! Glad it helped! :D
What if the integral is not simple in x and y and you need to break it up into multiple domains?
If I fall asleep to these videos with the playlist on loop, will I then be a math genius???
I'm not sure it works quite like that... but it's definitely worth a try! 😜
Do all integrals have the same volume?
What about if instead of the curves being our givens they already give us a triple integral and we have to change the order of integration, would this method work and how?
did you ever get an answer?>>
This is very very good. Thank you.
This is so good and still very valid. Thank you
Awesome explanation and great visuals!
Thanks, Jared! :D
Thank you for sharing this, it helps me a lot.
Oh good! I'm so glad it helped! :)
thank you so much! this is so clear and organized!
😊
This helped me a lot! Thank you.
So glad it could help!
My Prof. taught us this section, then told us to go home and watch your videos.
Thank you
Hi there. I have a similar question but the limits are defined by y^2 + z^2 = x and plane x=4. When finding the y(z) and z(y), we get y=√-z^2 and z=√-y^2 which is giving imaginary numbers. How would we proceed for such a problem?
Did you ever get an answer for that?
Thats indeed the perfection .. love it.. thank u ..
this is genius. Will it work everytime? i didnt see it in my book, thats why im wondering
+J Ferro Yes, it'll work everytime!
hi, u r really good at math. there's a subject called (volume integral) it's just like triple integral but with (divergant) or something can u explain it pls?
this is awesome..its like a machine...
+Thabang Joel :D
thanks so much
Thank youuuuu
Thank you so much!!! This has been really helpful.
You're welcome, Christal, I'm so glad it helped!!
thank you so much what an easy way
You're welcome, Abdo, glad it helped!
Damn!!! thus what i was looking for.Thanks !
You're welcome!
You said ''finding the volume'', you mean the hyper volume right??
thank you very much! :D
great video
Good job, thank you for the video!
Thanks!
Thank you so much. It helped me a lot.
You're welcome, Phuong! :)
wow i just loved the way you explained without a graph. I just have a question; what if there was y^2 in the equation instead of y. You would get two values of y from the equations and have 0 as given values so what will be the limits. And also if y was equal to something else say 2 instead of 0 would we still be substituting the value of y as 0 in the equation or should we consider 2 instead? please reply . thank you
+Sushant Bhatta If you had y^2, then you probably wouldn't be given y=0, so you'd use those two original values.
I have a similar problem and it does have a value of y. I am not very sure if u can really do these kindda problems without a real graph.
Thanks! Super helpful!
You're welcome, Joseph, so glad it helped! 😊
x^2 = 4, x = 2 not +/- sqrt(2)
pretty nice explained
Very helpful, thank you.
You're welcome, I'm so glad it helped!!
YOU ARE THE BEST!!
this was really helpful muchas gracias!
De nada, Brian, I'm so glad I could help! :D
saves me during corona thanks
This is so great, thanks a lot.
:D
Becker Lethc
So much helpful thank you so much 😍
You're welcome, Balaj! :D
Very very helpful
doesn't work with my functions.
perfect technic, Thank you
:D
This is awesome!
Aw thanks! I'm glad you liked it!
OMG THANK YOU SO MUCH
:D
very helpful. Thanks :-)
This helps "put it all together ".
:D
love love love ur voice!!!!
Madam is there is any pdf format available????
I have PDF versions of all my notes, quizzes, and workbooks in my online school. :)
@@kristakingmath are all those available in the online classes only?
At 6:20 sec it's not √2 just +/- 2