Answer:
4000 times greater
0^9 +7x+189yx−3y
o
9
+7x−3y
9
+7x+3y
9
−7x−3y
9
−7x+3y
9
+7x+189yx−3y
2 Collect like terms.
{o}^{9}+(7x+7x-7x-7x+7x)+(-3{y}^{9}+3{y}^{9}-3{y}^{9}+3{y}^{9})+189yx-3y
o
9
+(7x+7x−7x−7x+7x)+(−3y
9
+3y
9
−3y
9
+3y
9
)+189yx−3y
3 Simplify.
{o}^{9}+7x+189yx-3y
o
9
+7x+189yx−3y
Looks like we're given
which in three dimensions could be expressed as
and this has curl
which confirms the two-dimensional curl is 0.
It also looks like the region 
is the disk 
. Green's theorem says the integral of 
along the boundary of is equal to the integral of the two-dimensional curl of over the interior of :
which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of by
with 
. Then
