Answer
$c=d>b>a$
Work Step by Step
As the amount of region encircled by the loop increases, the value of the integral increases. Loop c and d both encircle the entire region, so the value of the loop integral is the greatest. Loop b has the second least area of the region encircled, so it has the second least value of the loop integral. Loop a has the least of the region encircled, so it has the least value of the loop integral.
