Double integrals to find mass and center of mass of the lamina (KristaKingMath)
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- Опубліковано 24 сер 2024
- ► My Multiple Integrals course: www.kristaking...
Learn how to find mass and center of mass of the lamina using double integrals. Use the double integral formula for mass and the double integral formulas for x bar and y bar to find center of mass.
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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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Krista you have single handedly taught me my entire calc 3 course. It is only thanks to you that I am passing! Thank you so much!
From the deepest part of a college freshman's heart, god bless you :')
😊
Finally a decent video that explains everything simply! Thank you
Is the X bar and Y bar correct? In the book the X bar is yp(x,y) and Y bar is xp(x,y) so im confused now...
Holly moly, it's test day and I've never heard of double integral! ahhh
O_o
It's an integral that you do another integral to
Not a big deal... my math proff certainly thought so since she gave us that treatment, casually mention double integrals like they're nothing
Thanks Krista. These videos, you post, help me prepare for my tutoring sessions.
Awesome! I'm glad you're able to use them to get prepared. :)
You're welcome! Glad I could help! :)
soooo helpful!!! at a pace I can actually understand (unlike my prof) & super clear!! thank you so much, makes my life so much easier
I'm so glad it could help! Thanks for letting me know. :)
thanks krista..i passed my test because of your videos..
+SiddheshDe Awesome! :D
Great explanation, very illuminating. Thanks!
+Ben Tulloch Thanks! Glad it could help!
Thank you for all the videos. Detailed explanation=full understanding , and that your way.
I'm so glad you like them!
Thank you! If only professors could explain things the way you do or Khan's Academy, life would be easier haha! :)
You're the best Krista!!
Watched this minutes before my test. It helped a lot
Oh awesome! I'm so glad it helped!
It looks hard but suddenly its simple!
You rock Krista!
Very clear and professional! Thank you
Find the mass of the plate in the shape of the curve (x
a
)2/3
+
(y
b
)2/3
= 1, the density being
given by ρ = µxy, µ being a constant. Please do this
can someone explain how she get the result of 3/4 and 3/2
Studying for my Calc 3 exam later. This video has saved my life lol THANK YOU!
You're welcome, I'm so glad it helped! Good luck on your exam, I hope you do great!!
Just finished the exam. Definitely helped!
Thanks, this is tough but doable thanks to your help
Had to search for solution like this for an hour... Thank You
I'm glad you at least found it! :)
Thank you so much for this. I never comment on education videos but this was bomb
You're welcome, I'm glad you liked it!
Well explained 👍 👍
Thank you so much, Kuldeep! :)
The p is actually 'rho', and it is expressing the density as a function of x and y.
You're welcome!
Crystal clear explanation....👍👍👍
you saved my life.. thank you so much!
it's not bad once you get the hang of it! :)
Great video, but what would the new limits be if say the top coordinate was (1,3) instead of (0,3). What would the new bounds be on y?
I haven't actually studied this in my first year, but it looks interesting. What does the function P(x,y) represent? Why is it specifically P(x,y)=x+y for this specific problem?
What program do you use to make these highly informative videos?
+Tyagadipta Biswal I explain here: www.kristakingmath.com/my-videos
Good video, very helpful. I think it might be more helpful if you explained why you integrated in the order that you did (dydx). Which I think is because this is a vertically simple region? Either way, it took some thinking for me to figure out why you chose the order you did, and it would be nice if that was explained better. =p
If you were to integrate with respect to x first, you would have to split the integral up into two integrals, one for the region above y = 1, and one for the region below.
Notice that when integrating w.r.t. x first, you have two possible equations as your upper limit.
Awww Krista! You have inspired me to make my own video for a math problem that I had a hard time figuring out. I went to tutoring. But yea....Im not as professional as you. I can edit myself though. I already recorded I just got to edit and upload. Thank you so much Krista!!! Even though I failed all the quizzes and midterms for cal 3 after seeing your videos I'm ready and I'm going to own the final...hopefully.
Very cool! I hope you can rock the final! :)
Thanks Krista!
I love you Krista
And what about moment of inertia ?
Welcome back. Nice new work.
you are awesome !! :) your videos coincide with my current class !!!!
+Philthy Phil (TheOriginal) :D
On the x coordinate you have an error you should multiply with y not x .Can you confirm that or it's on my side
Thank you 💖💖💖
Obrigado. Muito bom.............
Thank you so much!
It's Brazilian for "Thank you very much"
Good video...
what equation do you use to find the moments of inertia of the lamina?
Ben Paul This might help: ua-cam.com/video/bf_oNJ0jEUA/v-deo.html
thank you very much well understood
thnks
Awesome, thank you, great
This was great!
+toosikkid123 Thank you!
anyone else notice she has one green and one brown eye? Super cool! love your videos btw, helped me ace my final! :)
It's more like a green spot within an otherwise generally brown-ish eye, lol. :) Congrats on your final! So glad the videos could help.
Aww thanks! :)
this was very helpful.
Great! :D
Thank you
You're welcome! Glad it could help.
one of the best, thanks :)
I really appreciate what you do.Thanks
Your a Queen, thank you :)
OMG she gave you a heart
@@edwinsebastianperezrodrigu8659 yes I got so happy :) she has been so helpful to thousands of students literally:)) she is so humble and considerate
Cant we just use y boundary from 0 to 3? Why describe it in terms of x?
Your channel is amazing
Are we integrating by dy first in this case because the graph is easier defined by an upper and lower bound or in the case of looking for mass, we will always integrate by dy first?
Thank you!
what program did you use to write on the blackboard?
A lot of thanks mam
you're welcome!! :)
whether the lamina is referred to in this video there is a section on the bone?
Thank you, your really good in math 😂:)
:)
Thank you very much ma'am...
You're welcome! Glad I could help.
I have been saved.
nice solution
Thanks!
this is just great!
+MrFbi101101 Thanks!
thanks!! :D
thanks soooooo much
+Ahmed Hamada You're welcome!
Please,Do You Mind If You Explain Moment Of Inrtia .?
Thank You so much!!!
You're welcome! :)
Thank Youuu !!
thanks
thnx
I don't understand the power rule used for y= 1/2y^2. Please help.
Haha! Sorry! I got confused with differentiation and integration. I'll cleared up now. Thanks a lot for the video. I just wish I'd have seen this sooner.
do you mean the general form of the double integral?
why is p(x,y)=x+y necessary to know to do this calculation?
p(x+y) is the density which in this case is mass per unit area (density = mass/area) (and is not necessarily constant over the entire area). so you integrate p(x+y) with respect to area to get mass. (one could see that from mass=density x area)
you don't happen to have any videos for finding the centroid/center of mass with the help of triple integrals?
+Shahin Sateei You mean like this? ua-cam.com/video/_SYOyif-itE/v-deo.html
exactly, though that example was too easy :/ was hoping for something along the lines of "centre of mass for a solid in the 1st octant" etc.
+Shahin Sateei I'll try to add something like that. :)
Amazing
+尾生子煦 Thank you!
Thank you very much. :)
You're welcome!
amazing😍
i want to know how to solve definite integral when the intervals is variable
MVP!!!
I'm confused. My calc 3 professor said Mx = integral of the region yρ(x, y) dA and My is equal to integral of the region xρ(x, y) dA and X bar is equal to Mx/m and y bar is equal to My/m
Is there a difference or will I still get the same answer if I do it both ways?
brokenflightz the My /m =x
My =double integral x*p(x,y)da
this should be it it think
x bar is equal to My/m and y bar is equal to Mx/m, and My = xρ(x, y) dA and Mx = yρ(x, y) dA
yes do it the way your professor told you. Also do not integrate using dydx, you need to use dxdy
y=Mx/m in class in just the same as here... it is just that she already insert it in the equation in the first place. So her equation become X = 1/m ( MY )
Will the mass always be positive?
Yes
Why tho?
The only thing stumping me is the comprehension of the integral being a weighted average of the values, understanding x and y bar. The equations aren't intuitive.
The only intuitive equation to me was integrating density P to get mass.
Never knew Americans are good at maths
Beautiful and smart, what more can you ask for?
big fan
Thank you so much!
thank you
;)
You're welcome! Glad I could help.
good
Thanks!
What is your name and name facebook to help me ...Iam student master mathematic
Rebwar Mohammed smooth
What
😛😛😛😛😛
My queen...........
i got = 1/2*x^2 +xy
super like (Y)
Some new concepts here (roe?), but will take on faith.
I love your voice
I love you where are you from?
You are certainly the best teacher in calculus 1 and 2 but basics me she is a must in engineerings but some must have at least more than 7 years to become a nerd .in pascal maths is boring to death there is no logics maths the intecracies is just a weird mind bending .but creativity some had to have at least 6 to 8 years to pretend to be something unez to consider .even ivy are just ivy in their classical ways respectable.dimetimes is becoming boring in the sense of research and creativity .when you look at rafale or airbus 360 even shuttle it's me who design it and the crook Italian stole by mass murders by crooks lawers of that Rumsfeld ..and panetta the 2 make the pair .why we build rafele and airbus cause some nutties engineers with no purposes are out of jobs .just like I build the Lumineers to the president dean of fr professors cause our tenure masters in dentistry is out of job with no reason to be blundgoen by some nutties apartheid progressiste haters .dime just can't get it get yet that once the crooks are know by their tenuteoutrage if haters and prejudice the good ones are neither to fearcause some nwrds are recin by their peers and not the crooks mobs crial intentions of lavish underseval haters .
ρ should be used for triple integrals σ should be used for double integrals I think.
+anikoustos2 ohhh, how anti-establishment of you. edgy.
love u😘
great :p
:D
i love you