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# Example of calculating a surface integral part 2

Example of calculating a surface integral part 2. Created by Sal Khan.

## Want to join the conversation?

• This video without cursor is a bit confusing for me, i don't know where sal talk about when he say:
"that guy" but without the cursor i don't know what he's talking about.
• I was just about to complain about the same issue. I'm not sure if the problem is with the HTML player versus flash or if the video file is missing the cursor.
• Hello friends, I have an uneasy feeling about the way the computation is going. Sal created a parameterization of the torus in a left handed coordinate system and now he is taking a cross product which I think is defined only for a right handed coordinate system. In fact, the cross product essentially defines what is a right handed coordinate system. I am confident a better mathematician than I will suggest that it all comes out OK in the end, but I would be very reluctant to proceed in this way. Can anyone tell me why I should not be concerned? Best wishes.
• Good question, I didn't notice that he parametried it in a left handed coordinate system! Here's my thinking:

You can convert a left handed coordinate system to a right handed one by inverting the z-axis (imagine turning your left hand upside down). This transformation doesn't change the shape of the torus, it only flips it along the xy-plane. If we input some (s, t) into our left handed parametrization and get some point (x,y,z), this is equivalent to the (x,y,-z) in the right handed torus. The cross product is the infinitesmal area unit for an input (s,t). Since the torus is symmetrical over the xy-plane, the inifitesmal area unit in (x,y,z) and (x, y, -z) should be the same and therefore the orientation of the coordinate system doesn't matter for all inputs (s,t).

If this reasoning hold, this would only work for shapes symmetrical over the xy-plane and it seems like a much better idea to do right handed parametrizations when possible.

(1 vote)
• I thought that matrices had to be squared in order to take a determinant?
(1 vote)
• It is, we let the unit vectors < i , j , k > be the first row, then the other two vectors to be the 2nd and 3rd rows. Thus, it becomes a 3x3 matrix.
• At , he could have written (b+a*cos(t)) outside of determinant. Result would be the same, but there would be less writing, as you can divide one row (or a column) by some number, and than multiply determinant by the same number (in our case (b+a*cos(t)) )
(1 vote)
• Is it just me or can no one see the cursor in this and the previous video cause without it, it gets kind of hard to understand which term Sal is referring to when he says "this guy" and "that guy"