Line Integrals: Full Example

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FULL VECTOR CALCULUS PLAYLIST: • Calculus IV: Vector Ca...
This video is a fully worked example of a line Integral. We use the Line Integral formula to compute the Line integral of a function f(x,y) over top of a circle of radius 2. We first parameterize the curve, then write the function in terms of that parameter, and then substitute into the formula.
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Опубликовано:

2 окт 2024

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Комментарии : 71

@jgseg6828 3 года назад

Bro, you're one of the most formidable teachers I've ever met. Thanks for these lessons!

@dhrubojyotipaul2585 4 года назад

Your lecture series is really awesome. Please make a series on conics section that will help lot of students

@anasmikael5753 Год назад

Can I ask , how did you get (1+sin 2t) and how you get sqrt((-2sin t)^2 + (2 cos t)^2) become 2 dt ? Sorry I'm a new learner.

@ed8620 6 месяцев назад

There is an important identity in trigonometry which is really important for these problems, its sin^2(x)+cos^2(x) = 1 for any value of x. So that’s why it’s just 1 for the 1+sin2t bit, and then you have sqrt(4sin^2(t)+4cos^2(t)) you can factor out the 4, and then the identity brings the sin^2+cos^2 to 1, so you have sqrt(4(1))=2 Also the sin2t came from the double angle formula. It says that sin(2t)=2cos(t)sin(t) hope that makes sens😊

@arniedamaniac6206 Месяц назад

@@ed8620is this true because the sum of these values rooted is equal to the hypotenuse in the unit circle. Which is by definition 1?

@madeleinecallan3153 3 года назад

Currently a student over zoom in Calc 3. I have no idea what the book is saying. YOUR VISUALS ARE SAVING ME! Thank you sir 🥳

@literallynull 4 месяца назад

Exactly the same thing, we learn with Soviet textbooks and they are obscure

@a2_zhongbaode718 16 дней назад

Thank you for your lessons! I just love how lively you are and how you explain things step by step! Truely saving my university life

@hannananan9427 Год назад

I really can't believe that these videos are free to watch. God bless you, and your family!

@jasper3410 3 года назад

So, did we calculate the given area of the curve in this example? Anyway, thanks for the video. It really helps!

@jlpsinde 3 года назад

This is amazing, the visuals and you are a genius teacher. I am a physics teacher.

@edmund3504 3 года назад

Taking Mathematical Physics right now and these videos really help brush off the dust from those old calculus topics I learned a while back. Thank you so much :)

@anantjain9315 3 года назад

I am on a liking streak. thanks for these videos.

@DrTrefor 3 года назад

I like your liking streak!

@AG-pm3tc 3 года назад

These types of videos are life savers my dude, you earned a subscriber that's for sure. On a side note, maybe we are maybe a bit of a spoiled generation, with all the fancy computer graphics and great teachers the can feed us this knowledge with a spoon (it's like having the best privet teachers at your disposal always), which (IMO) actually hurts the solidification of this knowledge when you studying it for the first time (because you face less obstacles), but on the other hand, when you actually know this stuff, these videos are amazing to deepen intuition and refresh subjects quickly when they are relevant. Anyway, sorry for the mumbling, thanks for the great videos, i give you my respect a simple engineering student who tries his best to deepen his understanding of math.

@shashankrajashekar1672 3 года назад

Its important to analyse the topics visually than in equations...... Thanks for making it clear

@DrTrefor 3 года назад

Glad you liked it!

@Thadnill 3 года назад

Can't describe how much I appreciate this, I have my Multi-variable calculus exam in a couple of days and your videos is just what I need. Great animations, visuals and explanations!

@DrTrefor 3 года назад

Thank you and good luck!!

@continnum_radhe-radhe 2 года назад

I think your video is enough rather than a book 🙏🙏🙏

@nancyndaruga6428 3 года назад

hey nice video....I have a question though why when finding the height..that is the z component do you use f(x,y) instead of computing k directly..please reply ASAP

@ARKBlender Год назад

You do indeed teach amazing but i didnt understand a lot maybe because i just started it

@giannisfilippou7460 8 месяцев назад

lovely stuff. I am planning to take an aerodynamics course so i need some recap on math. You say in your first video that this is about 1/3 of your university course. When you say 1/3 are you referring to how many subjects you "touch" or how deep you go into each subject ? In any case i will surely be watching all the series. Thanks in advance.

@300risesagain5 2 года назад

Man why didn't I find your channel a little earlier?

@ryanmcginnis590 2 года назад

I believe you gave the wrong g prime of t and h prime of t, it seems u just left them unprimed. or am I missing something? either way it shouldn't change the answer since it is taken as absolute in terms of distance.

@ryanmcginnis590 2 года назад

oh actually I see after watching further u clarified my question cuz u wrote it right on the screen so disregard previous comment.

@continnum_radhe-radhe 2 года назад

Thank you sir 🔥🙏🔥

@mnada72 3 года назад

One of the topics dealt with blindly before but never visualized or understood. So line integral computes a surface area of a function over a curve, is it right?

@DrTrefor 3 года назад

That is one geometric interpretation yes, but there are several

@sophieczelusta3666 2 года назад

sir, you are a godsend

@adityaagarwal7357 10 месяцев назад

wow

@thebrightside2114 3 года назад

sir why we right sometimes velocity vector as it is in line integration and some times magnitude of velocity vector?

@DrTrefor 3 года назад

It just depends on whether we care about speed (thus take magnitude) or velocity, and thus want direction as well.

@dydx3741 4 года назад

that's really awesome explanation....I think you are born to be a teacher. really appreciate your work subscribed with Bell icon on 😊😁👍

@DrTrefor 4 года назад

Thanks a lot!!!

@dolly3883 3 года назад

No one can teach better than you thank you so muchh sir

@jordanfernandes581 4 года назад

Hi. I tried evaluating the integral at 5.12 and I'm getting 2pi as the answer. Am I doing something wrong ?!

@DrTrefor 4 года назад

Did you miss the orange 2 on the right?

@jordanfernandes581 4 года назад

@@DrTrefor I used U substitution on (2t) so I replaced the orange 2dt as du. The 1 integrated to 2pi and the sin(u) integrated to -cos(u) and evaluated to zero.

@jordanfernandes581 3 года назад

Ohh. I didn't distribute the 2 amongst both the 1 and the sin(2t) terms. I tagged it only with sin(2t). I get 4pi now. Thanks for replying 🙂

@rajat4260 3 года назад

Awesome explanation..thank you.

@GulzarAhmad-sw1kh 2 года назад

Good Explanation. I think it should be emphasized that circle at the bottom is a projection of the f(x,y).

@林士堯-d2c 6 месяцев назад

These series for calculus so a million times better than my college professor's. Why I'm not seeing this earlier?

@samuelhawksworth1923 Год назад

So I saw that line integrals are defined on a scalar field, is this an example of a scalar field? I haven't seen them before and am not too sure

@annushekhar6042 2 года назад

Wow you made it look so easy :)

@physicslover1950 4 года назад

Please do 1 video for optimization with line integrals like if we are given a multivariabe function f(x,y) and we have to compute its line integral from (a,b) to (c,d) then what should be the equation of the curve (over which the function is to be integrated) so that the line integral is minimum.

@infinix2003 2 года назад

i was able to solve just by seeing the question, thank you for your help in previous videos

@archimedes9851 Год назад

What represents line integral in vector calculas? (Mathematical meaning)

@gerardsagliocca6292 Год назад

Should show how you got the parametric equations.

@juliamacrae2245 2 года назад

Hello, trying to transition to multivariable calculus. I don't really understand parameterization. Why don't we define the curve C as x^2 + y^2 = 2^2. And why are vectors being used a lot all of a sudden, unlike single-variable calculus? I hope that makes sense.

@anshumanagrawal346 2 года назад

That's how the curve C is defined, indeed but to compute the line integral easily we need to parameterize it. You can watch the previous few videos in this playlist, I think they will help understand. For your second question, it's Vector Calculus of course we're gonna be using Vectors a lot