Line integral example from Vector Calculus

I discuss and solve a simple problem that involves the evaluation of a line integral. This particular line integral is in the differential form. The method used to solve this problem is one that involves a simple substitution. Such an example is seen in 2nd-year university mathematics.

[singh.ratan]

Thankyou very much.
Today i have decided to learn vector calculus only from you. Because i like your way to teach very much.
I have one request plz cover all topics of Vector Caculus because i m going to learn it only from you and if possible than Vector Analysis also.
Thanks again.

[voidsonvoid]

You are fantastic. Thank you for this!

[xenofurmi]

This is great. Keep up the good work.

[DrChrisTisdell]

@cesarcoronado747 Yes, I do understand Green's theorem and how it fits into the context here (eg, /watch?v=iwWQIKOLo7o&p=283CA2107AD503A3 ), however, it is not explicitly in the syllabus for the particular course that this video is designed for.
Best wishes
CT

[xenofurmi]

I now understand that this is a line integral of a vector field F(r) = - 9y ihat + 9x jhat through the curve given.

[xenofurmi]

@DrChrisTisdell One more comment, specifically about cesarcoronado747's comment. While it's a bit confrontational, it's a good comment in the sense that the combination of your video with his point (including a little bit of googling on my part) the fact that delM/delx - delL/dely = 1 means that you're finding the area enclosed by the curve (and then understanding that replacing 1 by other functions get's you places...) is a HUGE cognitive leap on my part.

[cesarcoronado]

Did you not realise that you were using the Green's Theorem area enclosed by a path formulae to calculate the area of half an ellipse?

[ZaxLaw]

why the e is anti-clockwise instead of clockwise?

[halcyon]

LOL I know that feeling; then at the end you may not even still understand it lol