Thankyou, so much for such a good explanation i was not able to understand this integration technique through any video on you tube except your video.You made this concept crystal clear for me.
If the determinant was negative, should I make it positive when evaluating double integral?, cuz i have a homework that contains two answers with the same boundaries but the determinant is negative
It's the same thing! You use the Jacobian whenever you change coordinates. When we switch from Euclidean coordinates to polar or cylindrical coordinates, dxdy changes to r drdθ. The r in front of drdθ comes from the Jacobian. You may not have been told that when you first learned it, but that's what it is.
We're not computing area here. To compute area of a region, we would integrate the function f(x,y)=1. Here the function is f(x,y)=x-y, which gives something else.
This is amazing, the best explanation of transformation!!!!!!
Thankyou, so much for such a good explanation
i was not able to understand this integration technique through any video on you tube except your video.You made this concept crystal clear for me.
keep going on upload the videos lots lo love from INDIA thank u sir for such a nice explanation
thanks, its help a lot
Thank u sooooooo much
Explained well
thank you very helpful
Great video! Clear speaking and nice handwriting, thank you!
@Andrew Bulba Thanks!
Love from India🤝 respect to you sir folding this in such less time with ease
mid sems?
The determinant would be -1/2. You forgot you write the negative sign. But thank you for your great explanation
he took the absolute value of the determinant
thank u so much for this video. it was very helpful! :)
btw anyone noticed that small hair on the paper?! lol
Rahhhh thanksss
If the determinant was negative, should I make it positive when evaluating double integral?, cuz i have a homework that contains two answers with the same boundaries but the determinant is negative
The rule implies that you put the determinant in absolute value
Why do we need to integrate using the jacobian coordinates? It seems more complex than cylindrical coordinates!
It's the same thing! You use the Jacobian whenever you change coordinates. When we switch from Euclidean coordinates to polar or cylindrical coordinates, dxdy changes to r drdθ. The r in front of drdθ comes from the Jacobian. You may not have been told that when you first learned it, but that's what it is.
@@andrewbulawa3273 Oh I get it now! So I can use any of these methods to find a volume of the solid including polar coordinates?
Lol, there "u" are. Classic. Too bad you weren't using "r" as one of the variables.
Isn't the primitive of 0 a constant ?
Thank you for the video
Indeed it is. But then when you evaluate the constant function, say f(v) = c, at -5 and -9 and subtract, you get f(-5)-f(-9) = c - c = 0.
Shouldn't the Jacobian be the transpose of what you wrote. Doesn't make a difference when calculating det though. Maybe I'm mistaken
I'm thinking the same too
Yes. You are correct. ..and what I was calling the Jacobian, I should have called the Jacobian Determinant.
I toughed the hair was on my screen hahaha
Haha! Keeping you on your toes!
So the area of the parallelogram is equal to 0? 😮
The x-y plane crosses the region R in a way that the positive volume is the same es the negative...add them and you get 0
We're not computing area here. To compute area of a region, we would integrate the function f(x,y)=1. Here the function is f(x,y)=x-y, which gives something else.