Stokes' theorem equates the line integral of along the curve to the surface integral of the curl of over any surface with the given curve as its boundary. The simplest such surface is the triangle with vertices (1,0,1), (0,1,0), and (0,0,1).
Parameterize this triangle (call it ) by
with and . Take the normal vector to to be
Divide this vector by its norm to get the unit normal vector. Note that this assumes a "positive" orientation, so that the boundary of is traversed in the counterclockwise direction when viewed from above.
Compute the curl of :
Then by Stokes' theorem,
where
The integral thus reduces to
I see no underlined digit. But here:
6 - Hundred place.
4 - Tens place.
8 - Units/ones place.
Answer: A,d,f
Step-by-step explanation:
Because you have to simplify the ratios of the colors.
I think it's 5 because 9 can go into 51 5 times with a reminder of 1 5 and 1