Great explanation.  One wouldn’t even need to know multivariable calculus to understand this.

Would be interesting to recollect how Jacobian is introduced, and how it's inferred in general

The reason for dxdy = rdrdθ is that dx dy is a small region of the rectangular plane, so we need to use the corresponding small region of the polar coordinate system. But the problem is that the area of the regions with length difference dr and angle difference dθ is not a constant, it's like the outer part of a sector, so we need to use the equation of sector area to figure out the area. The larger one has angle dθ and length r+dr, so its area is ((r+dr)^2 * dθ)/2, while the smaller one has angle dθ and length r, so its area is (r^2* dθ)/2, the difference will be (2rdr + dr^2)* dθ/2, and when we extract dr*dθ, the remaining one will be (2r+dr)/2. Since dr approaches 0 when the slices get smaller and smaller, (2r+dr)/2 will approach 2r/2 = r, so the final result is dxdy = rdrdθ

May God bless you, because it seems that you love to pass on your knowledge to others with love and sincerity.

The last part the best some people will say - or + but it is area 😂 and it is upper part of curve … congrats Hoca

OH MY GOD... What a brilliant Teacher you are sir.... my god... I didn't get anything but watich you is amazing....  i will learn from you...

Prove that dx.dy=rdr.d(Theta)

This dude has a natural ability to explain things the easy, understandable way. I watched 2 other videos of this same function prior to this one, but too many gaps in the explanation.

thanku sir what a explanation
😄😃

Excellent finally in my 80th. I understand the problem.

I remember when I thought this technique smacked of trickery. Then I learned of Feynmann's technique and the world stopped making sense altogether.

Ur greatest funny mathematican

i may not know that much math but your enthusiasm along with your amazing explanations in these videos makes it so easy to follow along :D

The Best! I'm a Brazilian fan!

Thank you so much  it helped me in the last minute 😊

Very smart. The result sqrt(pi) is related to circle or polar coordinates. Coordinates conversion simplifies the solution.

this integral is why i love calculus. you can really feel each step of the process and see why integration is so powerful. honoring symmetry, translating into polar coordinates, landing on a solvable form that provides such a satisfying answer. thanks prime newtons! never stop learning :)

Your explanations are perfect!

Very elegant solutions. Congratulations!!!

best explanation video so far however i think it would have been better to show change of variables more in depth using jacobian