This was honestly so so so helpful. From the bottom of my heart, thank you thank you THANK YOU so much. We need more tutors like you.
@m.donnediego5875 жыл бұрын
I like how you subtitle what you speak, it's helpful for me.
@wssz1128 жыл бұрын
dam now i want to go to MIT
@shi_shii_4 жыл бұрын
Who doesn't?
@martinrosol77195 ай бұрын
@@shi_shii_ You?
@ianmoseley99107 жыл бұрын
makes me realise how much I have forgotten in the 40+ years since uni. Expressing the integral in that graphic form was not something we were taught and it really helps me to grasp the whole concept; would have grokked so much more if we had been!
@rthelionheart3 жыл бұрын
In my school they simply say: evaluate the following integral just as given in part (a) above. It is entirely ALL UP TO YOU how you approach it. Of course one method makes life a whole lot easier than say compared to another one. It is expected that you know which method to use accordingly.
@beoptimistic58533 жыл бұрын
kzbin.info/www/bejne/rHenfpR-hpmejZo ...💐
@VocalBeast Жыл бұрын
Man thank you so much, literally the first time i actual properly understood polar coordinate transformations despite trying to wrap my head around it for like 3 months. Appreciate you!!!
@benn71397 жыл бұрын
his chalk is so big
@vtace16 жыл бұрын
it's sidewalk chalk, writes better.
@Tech4GamingIndia5 жыл бұрын
brother this is MIT
@PunkHippie19715 жыл бұрын
It’s girthy
@captainobvious14154 жыл бұрын
“Chalk”
@sambalder93433 жыл бұрын
mmmm
@AldenRyno13 жыл бұрын
@marcuswauson The integrand is [cos(theta)-(1/2)*cos(theta)] but when integrated, it becomes [sin(theta)-(1/2)*sin(theta)] from zero to pi/4. When evaluated equals sqrt(2)/2 - sqrt2)/4 = sqrt(2)/4
@muhammadzeeshankhan72518 жыл бұрын
Beautifully explained, I liked your teaching.
@morgard2113 жыл бұрын
These are actually very instructive excercises.
@beoptimistic58533 жыл бұрын
kzbin.info/www/bejne/rHenfpR-hpmejZo ...💐
@ashtongaeta25814 жыл бұрын
Thank you I have to study at home because of the corona virus. This came in so clutch!!
@mitocw4 жыл бұрын
Happy to help!
@DeprecatedAPI6 жыл бұрын
This was really awesome, thanks! Helped me in my end sems!!
@oliverbrace450511 жыл бұрын
dude, you`re awesome, i was able to do my homework thanks to you
@anikethsridhargund66712 жыл бұрын
Thanks a lot, I was struggling to solve a problem related usage of polar coordinates in my assignment, but now i solved it in just 5min. thanks once again!
@suruchisolanki36033 жыл бұрын
Thanks a lot MIT. I've finally understood the concept!!!
@shreyassahu69305 жыл бұрын
This is one of the best explanations for this topic.
@meerismailali60822 жыл бұрын
You don’t just cancel the r in 10:45. You solve for quadratic
@rkumaresh6 жыл бұрын
What a simple explanation which everyone could understand
@alexandresauve756011 жыл бұрын
yes; and this is how we deal with it. find the range of angles for which r is negative, split these segments away from your first integral and put a negative sign in front in order to find the area. example r=cos(theta) from 0 to 2pi gives negative r from pi/2 to 3pi/2. the area enclose by r=cos(theta) = integral of rcos(thta) from 3pi/2 to pi/2 plus (-) integral cos(thta) from pi/2 to 3pi/2. integrating the original function from o to 2pi gives 0 if you ignore the fact r goes negative.
@sairajbhosale39848 ай бұрын
This was so helpful to solve questions. My professor just solve 3-4 easy questions and left us with such questions Thanks a lot sir ..
@Jameel26313 жыл бұрын
@PeaceUdo Question a and b) The upper bound for y is y=x. The line y = x is always at a 45 degree (pi/4) angle with the x axis. If you dont get why, then for example lets say y = x = n (as y=x) then tan θ = n/n tan θ = 1 therefore θ=45 degree (pi/4)
@MCSPT11712 жыл бұрын
Because he has (1/r^3) r drdΘ, if you combine that r with (1/r^3) it would have a negtive power if you put it over one, (r has a power of one), therefore it becomes (1/r^(3-1)... and becomes 1/r^2. Hope this helps.
@23StudiosSports2 жыл бұрын
That helps sp much you have no idea, you are a legend.
@st.johntsuno-wayne24892 жыл бұрын
only in Calc BC trying to solve an argument with a friend when i found this… video made the concepts simple to understand and was extremely informative!
@Paulovrish73345 жыл бұрын
Finally, it makes perfect sense
@LICKSandWINKS11 жыл бұрын
I have an advanced calc exam on Tuesday AND YOU ARE A LIFE SAVER ILY
@edwinsebastianperezrodrigu86593 жыл бұрын
First time i watch a MIT class and i understand everything
@vrendus52211 жыл бұрын
To the instructor, thank you.
@NickZachPattyWack12 жыл бұрын
Not only do the brilliant students of MIT get excellent student teachers, but I can't understand majority of what my teacher says through his thick accent...and no my school is not well known even in the city that it resides in. Thanks David and MIT!
@DoggoWillink12 жыл бұрын
yeah, he didn't realize it was 1/r^3 when he re-wrote it
@anuraagkaravadi16409 жыл бұрын
limits explanation was awesome --which obviously is the heart and soul of the prob...lol in C in forgot to put square root.........
@HimanshuShekhar13s5 жыл бұрын
Mindblowing explanation! Thanks!
@quratulainfatima1097 жыл бұрын
Explained beautifully........
@GradientSoln-En7 ай бұрын
Thank you, just thank you.
@gnauhandy13 жыл бұрын
@marcuswauson you're evaluating 1/2 sin theta from 0-Pi/4.
@jbonn512 жыл бұрын
@maplestorypl He wrote it correctly. dA becomes r dr dtheta so the integral does become 1 / r^2.
@bhaktimd92994 жыл бұрын
What can be his age in 2011🤔
@joeferreira-qr7iq Жыл бұрын
the one thing i think that is missing when converting is that the F function at the end is not a function of x, y but r, theta you cant just plug in f given a function of x,y when in polar form
@usamafarooqi72922 жыл бұрын
Brillient.... Absolutly great
@MayankSharma-qd9ny3 жыл бұрын
Finally understood the concept
@vychuck9 жыл бұрын
Well done young man, really nailed it
@platinumk12 жыл бұрын
nice and concise. thank you david
@joshie9212 жыл бұрын
the -(1/r) can be changed to (1/r) if you swap the limits of integration, which is what he did here.
@Dhavalc201111 жыл бұрын
Best ! Like IT ! Simply ,straight forward and lucid :D
@WolfBoyBenRawr12 жыл бұрын
Thank you David!! This was extremely helpful !
@AbhayArsekar5 жыл бұрын
thank you so much David ❤️
@gabrieltmapondera96977 жыл бұрын
how is dxdy equal to rdrdθ
@adellewilliams32666 жыл бұрын
to prove this , we use jacobian method. And we all know that from cartessian to polar coordinate , x=cos@ and y=sin@ then dxdy change to drd@ and apply this to jacobian matrix (dx/dr dx/d@ , dy/dr dy/d@) then we get rdrd@
@molkgfmf56996 жыл бұрын
or... dA = (dr) (ds)? = (dr) d(rθ) = r (dr) (dθ) = (dx) (dy)
@AkashYadav-mr4hg6 жыл бұрын
use Jacobian
@JamilKhan-hk1wl5 жыл бұрын
There is a simpler method to understand that, dxdy is actually a very small square. So its equal to rdrdtheta
@АзХашми5 жыл бұрын
Look up the Jacobian for polar coordinates
@vinitamaharaj57387 жыл бұрын
Really helpful, thank you!
@marcuswauson13 жыл бұрын
cos of 0 is not 0, cos of 0 is 1, your answer to a should be (squareroot of 2) minus 2 all over 4. As cos of 0 is one, and one minus a half should give you squareroot of 2 over four minus a half.
@rain7492513 жыл бұрын
Thanks! I think you articulate it really well. That's awsome! Wish you're my prof. Not to be disrespectful, but are you an undergraduate? You look like a peer.
@erikumble3 жыл бұрын
In the introduction video of the TAs, David was a graduate student. Of course, that was 10 years ago.
@QuantumDisciple712 жыл бұрын
Very nicely demonstrated. I appreciate it!
@AhmadKhan-hb3je6 жыл бұрын
Nicely explained. But getting out of the board feels very awkward.
@HomoSapiensMember5 жыл бұрын
this helped me, thanks so much!
@hargeysasomaliland437412 жыл бұрын
Best lecture . Thanks for your kindly helping
@VikasSingh-cv2fu7 жыл бұрын
Good job bro. You really explain well.
@pedroff_16 жыл бұрын
I think somewhere in the middle of a.), you accidentally replaced 1/r^3 with 1/r^2 ...
@sumeepriya54544 жыл бұрын
Watch it again its correct
@ChucksSEADnDEAD4 жыл бұрын
It was subtle but you have to watch out for the 1/r^3 r dr dtheta. The r in the nominator position crosses out one of the rs in the denominator leaving 1/r^2 dr dtheta.
@syoushiro18376 жыл бұрын
at 10:33, you should not cancel the variable r because you miss the answer r = 0.
@sumitgupta69056 жыл бұрын
Best online classroom
@riya65493 жыл бұрын
is this the same as multiple integrals? im just starting out and im very confused...
@beoptimistic58533 жыл бұрын
kzbin.info/www/bejne/rHenfpR-hpmejZo ...💐
@русскийпартизан-ь6п7 жыл бұрын
I loved it! Thanks so much!!!
@femiairboy947 жыл бұрын
So how do you solve this if e^-x^2 is multiplied by Cos(bx) with respect to x
@ERLAANKABABU23BME7068 ай бұрын
He is a genius...
@nelsonlopez95875 жыл бұрын
MIT depends heavily on the chalk industry
@moasfco1113 жыл бұрын
thanks very helpful examples
@anjaneyasharma3222 жыл бұрын
Students note double or triple integration does not give correct results. Follow simple integration. The question is why count something twice as it happens in double triple integration.
@the_eternal_student14 күн бұрын
How did he know 1/(x^2+y^2)^1/2 was r? How did he know x^2+y^2=r^2?
@BlazeCyndaquil11 жыл бұрын
On the first one, shouldn't the result have been sqrt(2)/4 - 1/2? Wouldn't you have to subtract off the (1 - 1/2) from the lower bound of theta?
@ananyarathore46782 жыл бұрын
loveddd ittt!!! thankyouuu so much david sir
@pudingstorm18 жыл бұрын
Than you man, great video, simple and nice explanation :D
@prakharuttarpradesh3517 Жыл бұрын
Thank you professor You cleared all my doubts 🙏🙏 Dhanyawad and Namaskar
@rationalLeft10 жыл бұрын
I think there is a little mistake in the end of letter a). The result should be sqrt (2)/ 4 - 1/2, instead of sqrt (2)/4. Thank you for the excelent explanation.
@waltvanamstel680710 жыл бұрын
you have to integrate the 1/2*cos(θ), which gives you 1/2*sin(θ) integrating from 0 to pi/4. So sqrt(2)/4 is indeed correct.
@samuelminea55207 жыл бұрын
rationalLeft He had to integrate cos(a)-1/2*cos(a)=1/2*cos(a) which has the antiderivative equal to 1/2*sin(a) from 0 to pi/4 = sqrt(2)/(4)
@freakingik27812 жыл бұрын
Welcome back
@mustaphabouchaqour77705 жыл бұрын
for the last problem, it would be easy to switch the coordinate instead of x give y and so on.
@MarikoIchigo12 жыл бұрын
shouldn´t teta go from -π/2 to π/2?
@thecivilizedguy84254 жыл бұрын
Very clear teaching!
@darprahimi96927 жыл бұрын
Final answer for c) ??
@deepakkumarchandel24443 жыл бұрын
Excellent no one able to tell how limits of polar are going on.🙏
@johnpwnsyou11 жыл бұрын
No. There are several reasons why. First, r is a length, which logically can't be negative. Second, If you look at the formula, r=(x^2+y^2)^(1/2), you'll realize that there's no way for it to be negative since it's components are all squared.
@valkarez11375 жыл бұрын
youre stupid
@sreekarg95535 жыл бұрын
You’re replying to another comment aren’t you?
@ricardinhovorkes48766 жыл бұрын
Thank you thank you thank you I appreciate it a lot. Nice instructor very helpful
@celsiusfahrenheit11762 жыл бұрын
ARCTAN(y/x) when y==x is π/4 for the rest of us
@kamaraju155112 жыл бұрын
SUPER!
@zeldadu0911 жыл бұрын
Great Video!!! Greetings from GT!!!
@Dineshkumar-xv4xz5 жыл бұрын
Awesome thank you so much mit
@dant99446 жыл бұрын
why in example c teta goes only to Pi/2 = 90 and not to pi =180
@noahmckeever90599 жыл бұрын
In part a) why do you go from 1/r^3 to 1/r^2?
@AlexVX_9 жыл бұрын
he multiplied 1/r^3 by the r from "r dr d theta", leaving 1/r^2
@Lagos3sgte12 жыл бұрын
Great video! Really helpful.
@anannyauberoi79848 жыл бұрын
Thanks a ton!
@FirstGradeCalculus12 жыл бұрын
Great videos, David. Thanks kindly!
@matthewskatuta13053 жыл бұрын
Excellent work
@krishnaghorai81465 жыл бұрын
Good base ,so love you sir!
@aditkalyani79666 жыл бұрын
Very well explained!
@animeshpathak39215 жыл бұрын
how could you just assume the lower limit oangle of the parabola to be 0
@HereToday3210 жыл бұрын
how do you know the maximum line is pi/4?
@jeffreychang229310 жыл бұрын
Look at a unit circle. You see that y = x is half of quadrant one and quadrant one is from 0 to pi/2. and half of that is pi/4 so you get theta = pi/4 as your max theta value.
@hasanabs Жыл бұрын
Does the last example diverge? Because the the internal integration integral[r=0,r=2sin(theta)] r^-2 dr = -1/r | [r=0,r=2sin(theta)] = -(1/2sin(theta)-1/0) = diverge
@_tasneem73782 жыл бұрын
That was really helpful. Super clear!
@l1mmg0t3 жыл бұрын
I am an old man now. seems I can understand this better than my young age. feel like to go back to school.
@grovestreet91656 жыл бұрын
Perfect
@beercity12313 жыл бұрын
Worth the watch! Very helpful!
@sajathsalim2615 жыл бұрын
Oh my gosh.. Our IIT is world's best in terms of proffessor knowledge
@MohitSharma-wt9ex5 жыл бұрын
bro iit nahi VO MIT ka he . aur MIT no 1 he world me