tell u the truth..i studied this in 1975 and am now 59...Now I understand the damn line integral.
@sontapaa11jokulainen944 жыл бұрын
Congratulations!
@williamrubin9143 жыл бұрын
Me too
@objectoriented3049 Жыл бұрын
Now you're 70!
@frzy97012 күн бұрын
@@objectoriented3049damn
@dreia24057 жыл бұрын
It's fantastic how you summarize a one hour lecture in 15 minutes
@oximas-oe9vf2 жыл бұрын
lectures are sometimes unreasonably long
@oximas-oe9vf2 жыл бұрын
lectures are sometimes unreasonably long
@ChrisSudlik14 жыл бұрын
Thank you so much, these videos are about to save my education. I was struggling with line and surface integrals, and some physics electromagnetic stuff, The past few videos were great, and I really get the stuff now. It is really a great thing you are doing for people.
@md650006 жыл бұрын
The Khan academy drinking game: every time he says something about "not too rigorous" or "hand waving" you throw back a shot.
@TheFarmanimalfriend4 жыл бұрын
With a good bottle of Scotch, I would rapidly become unable to drive.
@stormyprawnАй бұрын
I'm not doing any maths after that game... Any good maths anyway
@thehorizonchaser10 жыл бұрын
If only I watched these videos before I started cramming for finals... Learning is so much easier when you aren't stressed haha
@neelmodi579110 жыл бұрын
thats my plan too
@Peter_19869 жыл бұрын
"Bah, several months before the exam, there is no rush." 6 weeks later "Oh yeah, that exam, maybe I should start studying now." Reads the first half. "I should probably review this first half, so that I really understand it." Two weeks before the exam. "Oh shit, I had better hurry now, let me see, I have a total of 30 sections to read, maybe if I read 4 sections a day and then practice old exams... or is there a better way...? Gah! Next time I will start studying in time!" Waits too long next time as well.
@battlewing2214 жыл бұрын
@@Peter_1986 i thought this was just me lol
@battlewing2214 жыл бұрын
exactly !
@bachabacha70483 жыл бұрын
@@Peter_1986 I'm watching this before one week 😹
@karan8538 жыл бұрын
at 10:53 , for small method we can multiply and divide by 2. so integral part will be 2sint*cost that is equal to sin2t.then integration of sin2t= -cos2t/2 .
@nikhilnegi94464 жыл бұрын
Lol, I was also thinking the same Bro in India we are taught so many small tricks to solve the problems
@astrobruce75854 жыл бұрын
Lol ya
@AhmedMahmoud-tv9vw3 жыл бұрын
nice one.
@griffisme48333 жыл бұрын
Or you can just know how integrals work and figure out that sinxcosx came from sin^2(x) and work backward relatively fast
@darkseid8563 жыл бұрын
Just solve it using gamma function . Even faster .
@theludvigmaxis17 жыл бұрын
Amazing job. I haven't even started calc 3 yet but I like to jump ahead. Very nicely done it managed to click and I have a very good understanding in line integrals now!
@EmpyreanLightASMR7 ай бұрын
I'm going to pretend you jumped ahead by 6 years and are going to take calc 3 next year.
@theludvigmaxis17 ай бұрын
@@EmpyreanLightASMR im actually a PhD candidate now, I took calc 3 probably the same year I watched this video. I was in highschool at the time
@erikmcguire548611 жыл бұрын
I wish my professors would teach like this!
@banshee51111 жыл бұрын
A good grasp of English would be a good start for mine...
@HAWXLEADER12 жыл бұрын
tip: try to hold shift while drawing a line to make it straight! it should work on all drawing applications... you are a master of teaching!
@fahadnazir89243 жыл бұрын
This video traces the journey of a super crazy integral becoming a super easy integral :-)
@LucifertheAtheist12 жыл бұрын
Thankyou ever so much sir. This whole KZbin teaching programme of yours is extremely benevolent. Thankyou.
@NiiAryee2 жыл бұрын
Line integral delivered in simple logical math. Amazing!
@ShayJorge7 жыл бұрын
Once again, Sal was able to teach me in 10 minutes what my college professor failed to in 2 hours.
@okktok6 жыл бұрын
Or maybe you just aren't paying enough attention
@Sherlock35412 жыл бұрын
It seems strange to me but even when I feel sleepy and I see his lectures I can understand even then!
@sandracordoba6090 Жыл бұрын
Your teaching abilities are beyond normal humans. Muchas gracias!
@AjayiPelumi5 жыл бұрын
Sir, you just earned my respect! I wish I saw this before my first exam T.T Nonetheless, I'm now looking forward to the next exam!
@nikhilgarg25789 жыл бұрын
ANYWAY.....SUPERB WAY OF EXPLAINING STUFF IN A SIMPLE AND LUCIS MANNER
@Seracinfinity13 жыл бұрын
You have a real gift for teaching. Very rare
@dreia24057 жыл бұрын
thank very much, you are an amazing teacher
@user-jk4jj4nm1q8 жыл бұрын
.. So what is Green's theorem?
@ShayJorge7 жыл бұрын
Lol he has another video on it, don't know why he put it in the title of this video
@MisterTutor201011 жыл бұрын
I used that method as well. sin(t) cos(t) can be integrated to -1/2(cos(t))^2 or 1/2(sin(t))^2. The answer comes out the same both ways.
@AWacademy5216 ай бұрын
Amazing tutorial. Thank you dear!
@parag18313 жыл бұрын
this video explains how radon transform work in ct scan... thanks a ton..u made such a complicated thing as easy as it can be...
@Nikifuj90812 жыл бұрын
I love it when the subtitles say "UNINTELLIGIBLE" in all caps.
@abdelrahimabdelazim69634 жыл бұрын
بارك الله فيك God bless you
@13Septem1314 жыл бұрын
Thanks a lot. Great explanation and example. Your teaching skill is great.
@erickjian70253 жыл бұрын
nice one Sal. I think there is a easier way for sint cost: d(sin(2t))/dt = 2sint cost
@goon55442 жыл бұрын
makes perfect sense. I don't really feel like seeing the advanced proof if I understand.
@anisurrahman54982 жыл бұрын
Thank you very much. That are the great explanation. ❤️
@tomasiscool14 жыл бұрын
@pmcmena1 no because he reordered the bounds to fit the u function; at the end of the video it wasn't "from t=0 to t=π/2", but rather "from u=0 to u=1".
@firozahmed84302 жыл бұрын
best teacher ever! 🔥🐯
@priyashanjayakody34132 жыл бұрын
You are an amazing teacher. Period.
@vulicuba80795 жыл бұрын
dS (differential arc)is fundamentally non linear in the picture but it being infinitesimally small, it can safely be assumed to be linear thus allowing its approximation by Pythagoras theorem. Is this point of view correct?
@tis_i_sana2 жыл бұрын
What was the need to do u substitution at the end ? It could easily be done by inspection...
@tomasiscool14 жыл бұрын
When you plot x(t) and y(t) on the 3d graphic, the quarter circle should begin and end on the x dimension extremity and the y dimension extremity of the cube, as in the function z=xy those extremities represent x=1 and y=1.
@aryamaansingh18949 жыл бұрын
Sal....u just saved my exam which is 3hrs from now...thanks a bunch :)
@l1mmg0t5 жыл бұрын
you are the best I wish 60 years ago my teacher can do this
@Hiei10413 жыл бұрын
Thanku very much sir for this and so many other videos..u are a great teacher..
@13Septem1314 жыл бұрын
hanks a lot. Great explanation and example. Your teaching skill is great.
@sandipsaha20906 жыл бұрын
How can we virtualized the line integral if f(x,y) is a 2d vector, example Electric field vector
@wediadi6788 Жыл бұрын
What a fantastic lecture.
@lawrencesibusiso74110 жыл бұрын
I LOVE YOU MAN!!!!!!!!!!!!(writing in a couple of hours!!!
@mmelkon010 жыл бұрын
Thank you very much. That was very well explained.
@davidash803 жыл бұрын
don't you have to put the values of u back into the equation after integration before finding the definite integral?
@minhvu88938 жыл бұрын
I like the software you used in the video very much, can you give me the name of it?
@aylora70333 жыл бұрын
i promise mr khan i will donate when i graduate ! 🥺💖
@suryavikramrizal34629 жыл бұрын
thank you so much Sal...
@MrCalhoun55615 жыл бұрын
If anyone wants to visualize vector and potential fields I suggest you to go to falstadcom. There is a java applet on this page which can generate these fields.
@akashverma57562 ай бұрын
Nothing is boring and tough to understand if your teacher know what they are teaching.
@yatharthsawarkar3607 Жыл бұрын
Excellent 🎉
@ninosawbrzostowiecki18929 жыл бұрын
you can also integrate sint*cost dt by converting it to 1/2*sin(2t) dt right? I did and got the same answer.
@aeroscience98349 жыл бұрын
Yes, that works too.
@santoslittlehelper069 жыл бұрын
+Ninosław Ciszewski You can use half-angles, but honestly, u-substitution is a lot easier.
@sebastianpearson78179 жыл бұрын
+santoslittlehelper06 if you knew the double/half angle formula it can sometimes save time in situations like this, it requires less working if you already knew the formulae
@cagataysunal11306 жыл бұрын
@@santoslittlehelper06 If you're doing calculus you should know your trigonometry.
@soumyajain69824 жыл бұрын
I love you 3000 for so nice teaching
@LucifertheAtheist12 жыл бұрын
I learn a lot from it.:)
@sarvagyagupta17443 жыл бұрын
I started watching this so late but correct if me I'm wrong. An application of this could be to calculate the surface area of mountains? We know the trajectory of a mountain and the width in each direction, so we can integrate the area under the curve wrt height at each point. Am I right?
@antoniofrancaib2 жыл бұрын
you are amazing man
@levmyshkin55903 жыл бұрын
Fantastic!
@lemons1072 жыл бұрын
Beautiful!
@firdushhussain70437 жыл бұрын
awesome...visualization
@078matthijs13 жыл бұрын
I had to pause the video saying that this is amazing!!!
@SanjayYadav-zb4lg5 жыл бұрын
Can't we use the dot product between the function and ds? It will make it more simpler, isn't it?
@TheGta4you12 жыл бұрын
Thanks Man (Morocco)
@robertwilsoniii20487 жыл бұрын
We just performed a line integral! F*ck yeah! :D
@123amouri7 жыл бұрын
Your videos are amazing !
@jadeitewu13 жыл бұрын
You Sir, are awesome.
@elbodi989410 жыл бұрын
befor i finish the video thnx realy it helped
@TheLionelreal11 жыл бұрын
if i consider a non parameterized function....like say i simply have y=x^2 ......should i parameterize it??
@MoonLight1102311 жыл бұрын
Thank you Sir.
@katiemcgatie12 жыл бұрын
I followed everything until the end - why didn't you replace u with sin(t) at the end of your u substitution and keep your bounds of integration in terms of t?
@MultiCoolman1257 жыл бұрын
It's a definite integral, so we don't really need to do that. We just need to evaluate it at those limits since the function is the same whether it is in terms of u or t.
@ghtkssk0112 жыл бұрын
Wow...that's great
@D_dusze9 ай бұрын
Brooo, im not even done with highschool and this now seems easy af
@abdelrahmanrashwan93926 жыл бұрын
could you recommend any book that I can practice solving more problems
@Peter_19864 жыл бұрын
You might wanna take a look at the book "Calculus: A Complete Course" by Adams. Also, the site "Paul's Online Math Notes" has lots of sections for Calculus 1/2/3, with example problems and everything, and the KZbin channel "Professor Leonard" is a fantastic channel for those exact courses, with tons of full lectures by an amazing teacher.
@yichizhang7959 жыл бұрын
Thanks!
@liam50106 жыл бұрын
can anyone tell me what software he used to trace the f(x;y) curve please?
@CliveReyes12 жыл бұрын
What do the colors in the 3-D plane stand for?
@hackman-hackman5 жыл бұрын
Achmed that’s actually a good question. They don’t stand for anything, it’s just a very smart way to tell you, the viewer, the direction of the slop and help you visualise by looking at the colour gradient.
@runiyobeen128 жыл бұрын
pretty neat
@rdevg6 жыл бұрын
amazing.......
@DrummerRF12 жыл бұрын
Yes
@HotPepperLala14 жыл бұрын
wow when I retire, I think I am going to join khanacademy
@Skystrike707 жыл бұрын
9:45 giant OH moment
@Kopfgeldjaeger600011 жыл бұрын
You make wonderful curly brackets!
@lampardiphosphorous8566 жыл бұрын
2:08 Sal said sqrt(2),sqrt(2) but meant sqrt(3)/2,sqrt(3)/2
@cavver35236 жыл бұрын
Lampardi Phosphorous No, because 45°=1/4π and sin(1/4π) & cos(1/4π) = sqrt(2)/2
@jcnotnot81205 жыл бұрын
If you switch the variables back to t’s after the substitution you get -1/2, why’s that?
@dorol6375 Жыл бұрын
I solved it with the identity sin(x)cos(x)=sin(2x)÷2
@sumeetbvarma11 жыл бұрын
Thank thank
@billydagenham12 жыл бұрын
I hope when my teacher eventually sees these videos he realizes that he's a incompetent union protected lower and commits hari kari
@melindaliao413611 жыл бұрын
I'm counting on your videos to get a 7 on calculus
@joshuaminnies13886 жыл бұрын
Been doing line surface and volume integrals for 2 months now only to realize now that the line integral is the area of the surface about the line. Face palm?
@Ditiro10011 жыл бұрын
what software or device is used to make this videos?
@ssayyahh5 жыл бұрын
Can you help me with this question? The value of the integral of the function g(x,y)=4 x^3+10y^4 along the straight line segment from the point (0,0) to the point (1,2) in the xy-plane is? My answer with your method is coming 33*(5^0.5). ds part is coming as 5^0.5. The correct answer is being shown as 33 only. Need help?????
@fahrenheit2101 Жыл бұрын
4 years late, but did you ever find out? I just tried it and I get the same as you.
@tahagargoum62478 жыл бұрын
hi to everyone sir just I want to know how you got this limits and how can I find it in other examples ?thanks
@somebody40618 жыл бұрын
The limits for "u=1" and "u=0"? Look up his videos on u-substitution.
@somebody40618 жыл бұрын
Basically, sin(0) = 0, and sin(pi/2) = 1.
@curiousminds3017 жыл бұрын
Why you dont resubstutute sint in place of u
@TuningFreak236 жыл бұрын
Why did he use substitution instead of the product rule for the integrations of sin(t) *cos(t)
@boyuanchang87089 жыл бұрын
Thank you
@bb485611 жыл бұрын
Why not mention that the factor you replace ds with is actually the length of c'(t) ?
@muneneantonym10853 жыл бұрын
good work sir,, otherwise make the video more visible
@lariosphotography47216 жыл бұрын
I understand the concept, proof of the formula and the results. But my question is, how is this useful in real life applications?
@thevegg32757 жыл бұрын
Sal. It seems you plugged the equation for the curve into where I thought you said the equation for the ceiling should be. I thought you said the ceiling was x times y but you've made it the exact equation for the floor.What if you have a problem where the equation for the ceiling is completely different than the floor? In other words, the f(x,y) (ceiling) should only be x times y not cos t times sin of t. What am I missing here, please? You cannot define the ceiling as a function of t, only the floor curve.
@computerchemistry22110 жыл бұрын
Do contour integration
@OneOfTheManyJason5 жыл бұрын
why don't we just use double integral? looks like it can give the same area too
@265HITMAN26513 жыл бұрын
your waaaaayyyy too slow, people aint watching to learn how to integrate, they're watching to learn about line integral, but the explanations are superb, very intuitive :P