Answer:
2261
Choice 1
Step-by-step explanation:
Took the quiz and got this as the right answer :)
By Stokes' theorem, the line integral of over is given by the surface integral of the curl of over , where is the region of intersection of the plane and the cylinder with having positive/upward orientation.
Parameterize by
with and .
Take the normal vector to to be
The curl of is
Then the line integral is equivalent to
Slope: -1/3
Y-intercept: -6
x + 3y = -18
x+18 = 3y
-3y/-3 = x/-3+18/-3
y = -1/3x - 6