Line Integrals - Evaluating a Line Integral

[shayan22h]

thank u ;)

[iceman10101]

MORE LINE INTERGRALS EXAMPLES

[yaboyjruff]

this was extremely helpful. thank you.

[phenethylaminedreams]

Real men use Spivak :P

[DjRipEntertainment]

why don't you change u back into sin(t)?

[cptcolo]

Yes please add Stokes Theorem!!! Professors should teach like this, with examples ready and neatly prepared. I would just play a video for the class to watch everyday and fix them over the years.

[MrEdwards01]

Could you do some videos on contour integration please?

[jamie1234591]

@patrickjmt

Hi, Just wondering if you can help throw some light on something that's bothering me...

Ok

You know that

Int(-inf to +inf of exp(-x^2)) = sqrt(pi) But this is ODD don't you think. Pi => Circles! What's the Gaussian got to do with circles.

I know about the change of variables trick and WHY the pi occurs, but physically if you will, where's the circles in the gaussian??

Hope this makes sense, Jamie.

[Go2Balen]

I just did this problem in my homework... and now I'm watching him do it... at least I know I did it right!

[sharinganfuranku]

Wow, this is the exact problem I was doing for homework! Lucky me!

[elmaslocotex]

thnx to your videos i don't faint during midterms no more

[gramshakja]

First i want to say thank you for all your videos. you are a life saver. I am taking Calc 3 now, and i am stuck to the part where we find t(0) and t(1) the limits of the integral to find the area of a loop. I was wondering if you could help me. Thanks again

[deltaklm]

Everything seems smooth but why didn't you plug the U= sin(t) back into the integrant at the end??

[deltaklm]

@deltaklm Nevermind, should have thought that one out before I asked. We plugged the limits of integration into U for a reason ;]

[imvanessavella]

decent example ;] thnks!!

[Incognito6543]

Could you (or anybody else) tell me which marker/pen do you use

that allows you to erase stuff right off the paper?

[demerda]

@Incognito6543

AHAHaHHAH freaking noob! Its not a paper.

[wesKokigen]

can you upload a proving video? I think if you proved the line integral formula it would be easier to understand, in my opinion.

[DSnyd601]

could you have used F dot dr here?

[varung92]

I am not a fan of the stewart textbook :/

[maqrux]

@varung92 It's a bit simplistic, probably the most simplistic of the bunch.

[dailydesi]

u r a cheetahhhh

[PoCripple]

Why can't I get a degree if I learn it all for free online?

[smallsmiles181]

I thought that was the Path Integral? What's the difference between the Path Integral and the Line Integral? I thought magnitude of c'(t) means Path Integral. Help?..

[whoppix]

@smallsmiles181 Path integral, line integral, curve integral and contour integral are all the same things.

[Sh1Math]

great



[ZhangyXD]

lol "pull it out" XP

[Cruth8987]

yeah.. what IS your preferred calculus textbook? I use larson..

[patrickJMT]

@Cruth8987 me? i do not have one.... larson seems good; i used stewart's as a student and also as when i lectured (bored people, that is). i think it is an ok book

[n7275]

@patrickJMT I used Stewart's as well.

[rawadom]

Oh no, it's just the module not absolute value, haha

[rawadom]

That square root is the absolute value of the derivative of f(x(t),y(t)) with respect to t

[jakelcab]

dang, my teacher sucks at explaining this compared to you.

[Czeckie]

@jakelcab Maybe your teacher really does, but ... are you talking about serious math course? It definitely takes a lof of time and technical, formal details to define line integrals properly and it takes even more effort to deriving the basic theorems and formulae for computation (which are used in this video). Give your teacher some love :)

[christine9944]

Such a great video! I found it really helpful :D

[patrickJMT]

@afghanplayr20 yes, you should look over your calc 2 stuff if you do not remember; there should be some basic examples in your book somewhere

[Picouchu]

patrickJMT CAN divide by zero

[arias1772]

2:19 radius if four not sixteen

[seeker7truth1]

Man I sat here for like an hour trying to figure this very problem out, and you set this problem up and I realized what I did almost immediately...I felt like such a bonehead. Thx man, you explaim things sooooo much better than my current professor.

[ZhangyXD]

f university profs they are so fing useless

[thomashamiltom]

i have a similar problem, paramatizing from (0,1) to (-1,0) clockwise on the unit circle for F(x,y)=yi+xj. When paramatizing for circles like this, will we always choose x as cos(t) and y as sin(t)?

[ZhangyXD]

@thomashamiltom ya remember x=rcos(theta), y=rsin(theta)? theta = t(time) now

[thomashamiltom]

@ZhangyXD I can see it being easy like so for circles like this where 4 is the radius, but what about an elipse where the radius changes?

[JBS90]

I know you hear this alot, but I just don't understand why other professors can't be like you. You make everything seem so clear and sooooooo much easier to understand. Thank you so much for your time that you have spent making these videos. By the way, which book are you getting these problems out of? Because some of the problems are the exactly the same in my book. I was just wondering if you're using the same book as me. Mine is Essential Calculus, Early Transcendals by James Stewart.

[patrickJMT]

@JBS90 glad you like the vids. do not worry though, when i taught i am sure plenty of people said i sucked. yes, i am using stewarts book (my old version 5 edition that i taught from)

[arias1772]

@patrickJMT so are you anti rogawski? i heard stewart is good

[heimdall116]

@patrickJMT Doesn't appear to change much...I'm using Stewart 6E at Ohio State, and this is problem 16.2 #3.

[stonefree87]

If you're not an actual professor or working towards becoming one, you should really consider it. You have a gift for teaching people. Thank you very much!

[DeluxeWarPlaya]

This video helped me understand what a line integral actually is. That bit at the beginning about integrating the function around the curve C really helped. My maths professor didn't explain that bit. So in comparison to a regular integral, integrating about the x axis, instead of finding the area between the function and the x axis, we're finding the area between a function and some other line.

IT ALL MAKES SENSE NOW!!!

[loohz]

Nice. Thanks.

[patrickJMT]

@canhazthought not only beautiful, but smart! i like that. : )

[metaserve]

This video was so engaging, not even the star craft II ad could distract me.

[VWinUgo]

ily

[demondim5]

hahaha, was practising line integrals not 2 days ago and did this exact question (james stewart, calculus, 6th edition, sec 17.2 Q3.) had a little chuckle to myself. i actually had to check it when i did it because i didnt expect it to go so high.

[baigali93]

My final Calculus paper's coming and your uploaded videos are really helping me out of this jail.....keep it up

[ifstatements]

you say you want the radius to = 16 at 2:16 , but you want r^2=16 therefore r=4.

Thank you for the video!

[Knightmetal]

Hey Patrick, will you marry me? I'll be a good husband, I swear.

[Christillusion6sic6]

god bless you man youre the best!

[howfishhao]

Awesome video as always. In 2:17 though, when you said the radius had to be 16, did you mean 4? or...

[Dancesux]

Hey patrick what can you do when you end up with a term like 180t^2 + 128t3 under the root sign?

[adheeshz]

Cheers, Pretty Clear stuff. but erm.. i dunno how you just guessed the limits from -pi/2 -> pi/2 .

[zep4life]

intense. thanks for the help!

[crawfish35]

good video. it's actually "parametRize" and "parametRization", not "parametize" or "parametization". keep it up!

[Tribute0427]

Thank you so much! I wish my professor was as clear as you are in your explanations :)

[zechenife]

Very well done man, thanks for doing that.

[jaymofly8]

simple and effective video , thanks!!

[StarlightForOneYear]

can we use x = 4*sin(t) , y = 4*cos(t) ?

[supuwamigosh]

you r a life saver.

[limejello2525]

its not technical stuff...for the parametrization hes just using polar coordinates to integrate  (x = rcost and y = rsint) !

[superjini777]

i can't understand the Parametrization part!! please guide me through that..... lmao i've my exam after 2 days and i still dont know it..... please guys help

or i'll be hung to probation.....

[superjini777]

HI one dummy question but long story why im at this situation ......

Please Guide me ANY ONE!!!!

how to calculate r(t) for parametrization!!

its urgent! please buddies, ur help will be highly apreciated! reply with any "link" on statement.... please use beginners language for me!!

[starsing815]

Thanks very much... really helpful!!!

[FalconPictomancer]

thanks so much; i thought i was doing it completely wrong but this showed me the minor mistake i made. calc 3 final is tomorrow; i'll have you to thank if i do well

[matiomatio]

thank you

[jamescboyd]

Thanks dude. About to take Cal. 3 test 4... Then the final in a week. You're a lifesaver. I will forever remember the blessing you were to me in Cal. 2 & 3. Wish you had good differential equations videos for next semester! I haven't found them yet...

[jenn9580]

Thank you!!

[TuscanWonder995]

Thanks ... I was starting to hate mathematics after taking calculus 2.... But tanks to u, I can understand the physical representations of the mathematical symbolisms of these complex concepts...;)

[h8r4rlzyee]

thanx burbur... jus solved a problem i was stuck on for 30 mins..... yee

[mustangdale2001]

Your videos are the best. Id never make it through math with out this help.

[geoengstudent2013]

Your videos are way better than my prof's lectures. It's gotten so bad that she has just stopped lecturing and is using MIT videos as a stand-in.

Thanks for all of your hard work and keep it up!

[The6ChickMagnet]

hahahah what a horrible teacher

[sfcsarah]

Thanks for making this video, you make this otherwise complicated math lesson very short and easy.

Btw, your use of erasing and rewriting different parts of the evaluation is very effective.

Thanks again

[lilmayn2390]

it took my professor two classes to explain this and you just did it in less than 10 min. thank you!

[liquidstl]

I think thats because the profs. like to go into all teh technical stuff... Also this was showing how to do a line integral with respect to arc length ds. Still a great, clear video though.

[Vonpink15]

Patrick, thank you for posting. I found it very useful.

[searcherT]

This was a fun class calc II once i got the right prof 1st a hole used to spank over proofs I hated his ass cuz we saw nothing practical. I dropped and took next semester with an American and it was a rockn claess.

[Freestyler717]

You explain things so clearly. Why is it so hard for professors to do the same?

[patrickJMT]

perhaps they can just play my videos in all calc classes : )

[inspiration4him1]

My last calc teacher did lol.

[patrickJMT]

really?? hahaahh!! very often?

[vop3766]

this is path integral. not line integral -

[loki153624]

you rock... come teach in brisbane for a while lol you'll make my life easier... nah good work man keep it up!! Thanks!

[yashar22]

i am VERY greatful.

you basically just summed up my 1 hour class in 10 minutes

you should consider being a professor yourself

[hellrell102]

dude u fuckin own i had that question on my assignment and had no idea how to do it

[JamesNorton1234]

ha that problem's in my calculus book. wish ya had done #5 instead of #3. i got this one right :)

still very helpful keep it up.

[TheMaskedDonut]

Can you solve a line integral without the parameter "t"? I've got aproblem where the Vector field (Force)is F(x,y,z) = (f(x,y,z),g(x,y,z),h(x,y,z)) and the curve is r=(x,y,z) I can't see anyway to set this problem up without the parameter, but the question never mentions it, I don't suppose you're not busy and could reply with a simple relevant yes or no.

[samuelthestrong]

well thanks!

[calvinhobbesliker2]

is there a way to calculate the length of the curve of a function of x and y which is above a specific curve in the xy plane? Basically, is there a way to find the length of the green line on the top in the picture at the beginning?

[Lyubyashaya]

Hello, Patrick!

I appreciate ur work and really love your way of teaching, your way of representing everything!

I really love ur work and love you even more :) Don't get me wrong!

Thank you for ur effort! God bless you!!!!!!!

[patrickJMT]

thanks for the nice words : )

i am glad that i can help you!

[HiImWilfrdBrmly]

Im confused why the limits of integration changed?

[Zalzal019]

Because he is integrating in terms of u not t so you have to change the limits.

[headdytube]

nice job

[swraman]

Thanks, very descriptive! esp the geometric interpretation at the beginning

[musical17]

thanks, helped so much. keep it up :)

[mypainturass]

great video pat, REALLY NEED A STOKES THRM. VID, please please pretty please :D

[patrickJMT]

i need to read that physics book i bought first... : )

[mypainturass]

could you just do something on curlF, green's thrm, and stoke's thrm. I sorta understand the concept of flow circulation and flux, but it doesn't really matter in cal 3. what does matter is how to set up the problems with parametrization and knowing which cross products to take which i'm struggling with, you saved my ass in cal 2, i know you can do it again in cal 3! :D

[deepbluetarget]

pretty good example. nice vid.

[fmadero]

patrick:

What about this example

Integral(-4dy + 3dx) where c is a union (0,0) to (-4,3) and (-4,-3) to (-8,0)

[zeedee775]

These are awesome! You have a very clear, concise way of explaining things. Thanks for taking the time to make these.

[patrickJMT]

no problem. glad that they help

[tarang1990]

thanks a lot although i was able to solve the sum before you finished explaining it cleared watever doubts i had left..

[patrickJMT]

happy to help! you are too fast compared to me!

[tarang1990]

well thanks but i am getting by somehow my uni's SEM 1 math course... studying line surface multiple integrals right now.. thanks anyways!

[Waranle]

Thank you alot Patrick!

[patrickJMT]

no problem! : )