Notice that Given that 
is an ellipse, consider a conversion to polar coordinates:
The Jacobian for this transformation is
with determinant 
Then the integral in polar coordinates is
where you can evaluate the remaining integral by substituting 
and 
.
Answer:
I think 7=2, 6=-2, 4=23, 8=-7, 3=9, 1=12, 2=0, 5=7, 10=8, 11=3, 12=-45, 9=25
Step-by-step explanation:
I tried my best
1. 1/9 since you take all the "a"s in the words which is 2/18
2.2/9 same thing as above
3.18/18 since there is no "O" it's a trick question
4.3/9
5.5/6 since you don't count 6
6.1/2 and 1/2 coins are always 1/2 unless you flip twice
7.5/13
8.1/2 because 1,3,5 odd 2,4,6 even
Hope that helps
