Page 128 slopes and intercepts
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Use Stokes' theorem for both parts, which equates the surface integral of the curl to the line integral along the surface's boundary.
a. The boundary of the hemisphere is the circle in the plane
, where the curl is
. Green's theorem applies here, so that
which means the value of the line integral is 3 times the area of the circle, or .
b. The closed sphere has no boundary, so by Stokes' theorem the integral is 0.
Actually it's
y =
it's a line. so 2 points is enough
choose x so that x+4 would be divisible by 3 :)
1) x = 2, then y = (2+6) / 3 = 2 - sketch point (2,2)
2) x = 5, then y = (5+4) / 3 = 3 - sketch point (5,3)
3) line goes though those points. use ruler :)
y =
it's a line. so 2 points is enough
choose x so that x+4 would be divisible by 3 :)
1) x = 2, then y = (2+6) / 3 = 2 - sketch point (2,2)
2) x = 5, then y = (5+4) / 3 = 3 - sketch point (5,3)
3) line goes though those points. use ruler :)