a=b=1;rth=10;c=d=8/SNR

f(SNR)=(d/4)^2*int((int(x^(a-1)*BesselK(2*a-2,sqrt(d*x)),x=0..rth*(y+w)/y))*y^(b-1)*BesselK(2*b-2,sqrt(c*y)),y=0..infinity))

f(SNR) is a non-increasing function of SNR。The value of function f(SNR) become negative when SNR is larger than 700.but  if I use mathematica to calculate this function ,the result is always positive when SNR is taken from 0 to 10000.why?