If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# 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 thought that matrices had to be squared in order to take a determinant?
(1 vote) • 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) • Wait so why do we have to take the cosine of i hat? is i hat supposed to be x vector?
(1 vote) • I find the approach of alternating + and - for sub-determinates confusing, and prefer to either actually copy the first column as an extra column to the right (I think that's how I was taught long ago), or to just think of it as being there, so the pattern of the operation always stays the same (upper left x lower right) - (upper right x lower left) in each case. I think that's also consistent with the Levi-Civita symbols, which I don't quite understand, but look like lower case epsilon, and through some symmetry rules that determine which indices are -1, 1 or 0, apparently prescribe the indices in a compact way so that the cross product can be represented as a simple summation, and also lead to some (apparently) useful identities when combined with the Kroneker delta operator for the dot product. So not a question I guess. More of a comment, but I would like to have the Levi-Civita symbols explained. The source I have is completely cryptic and basically fails, though i*(A2B3-A3B2)+j*(A3B1-A1B3)+k(A1B2-A2B2) is the outcome.
(1 vote) • 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.
(1 vote) • what are those, adidas or nike or what? 