In the first part of example, at time 8:40, when you were integrating between 0,2, you took f(x) only, which equals f(t), why you did not take f(y) also, ? or is it because we are asked only for x, since z= x. Thanks
I don't understand at 10:25, how can a curvy line be put onto a straight surface, isn't that the reason why the map of the earth is so inaccurate. We can't put something curvy on a straight plane.
The method that I presented here is for integrating a given (explicit) function f(x,y) over a given 2-dimensional curve C. For some applications it might be necessary to solve for f(x,y) from an implicit equation!
As a math purist, I'm disappointed that you resorted to "velocity" to convert ds to |r'(t)| dt when this is just a straightforward computation of arc length ...
I find the *r* - *v* - *a* and | *v* | = ds/dt relationships extremely useful for intuitive problem-solving, so I'm always happy to see them put to good use :)
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In the first part of example, at time 8:40, when you were integrating between 0,2, you took f(x) only, which equals f(t), why you did not take f(y) also, ? or is it because we are asked only for x, since z= x. Thanks
See 8:28. We're given that the function is f(x,y) = x.
beautiful explanation!
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Clear and concise...👌...A new subscriber
very good explanation. the examples selection are very good
Wow ,you are doing a terrific job explaining math ,I hope that I should be fluent in math like you one day
Very Helpful. Thanks Gentleman.
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Such a beauty
I don't understand at 10:25, how can a curvy line be put onto a straight surface, isn't that the reason why the map of the earth is so inaccurate. We can't put something curvy on a straight plane.
Right, and that's why taking the line integral with dx or dy is DIFFERENT from taking it with respect to ds. You're calculating a different area!
Great. Thanks 🌍 from Johannesburg.
saved my life
Thanks a lot
Can you explain definite Integration of The greatest integer function?
Love from India
See this video for an explanation: th-cam.com/video/5gtf9OuHa9Y/w-d-xo.html
what if the curve is a closed curve ?
Thanks for such an amazing vedio.
Can we say that the explanation given by you was solely for explicit functions 《z=f(x,y)》 ?
The method that I presented here is for integrating a given (explicit) function f(x,y) over a given 2-dimensional curve C. For some applications it might be necessary to solve for f(x,y) from an implicit equation!
The integral you get is the magnitude of the vector valued function prime with the limits plugged in?
It's just the magnitud of the curved area
I am annoyed that we never covered vector calculus in freshman year. We didn't have computer graphics back then, but it's no excuse.
love from India
As a math purist, I'm disappointed that you resorted to "velocity" to convert ds to |r'(t)| dt when this is just a straightforward computation of arc length ...
I find the *r* - *v* - *a* and | *v* | = ds/dt relationships extremely useful for intuitive problem-solving, so I'm always happy to see them put to good use :)