Consider K(x, y): = (cos(2xy), sin(2xy)).
a) Compute rot(K).
b) For a > 0 and λ ≥ 0 let Ya,x : [0; 1] → R² be the parametrized curve defined by a,x(t) = (−a + 2at, λ) (√a,λ is the line connecting the points (-a, λ) and (a, X)). Show that for all \ ≥ 0,
lim [ ∫γα,λ K. dx- ∫γα,0 K. dx ]= 0
a →[infinity]
c) Compute ∫-[infinity] e-x2 cos(2λx) dx