Q2 (10 points) use the green-stokes formula in order to compute the vector line integral: (z + y') dx + (2x - z) dy + (x- - y) dz where t is the triangle with vertices (1, 0, 0), (0, 1,0) and (0, 0, 2) traversed in the direction implied by the order in which the vertices were given (i. e. from the 1st to the 2nd, to the 3rd and then back to the 1st one).

has the underlying vector field

with curl

Parameterize by

with , .

The implied orientation of the curve is counter-clockwise when viewing from the first octant (each of greater than 0), so that the normal vector to is pointing upward and away from the origin. Take this vector to be

Then by Stokes' theorem, the line integral is equivalent to

step-by-step explanation:

for exempl this   system of equations   y = x - 3

                                                                y = 2x - 5

look   the line : y = x -3     ( red)

                            the line : y = 2x -5 ( bleus)