The F-distribution for f (the ratio of reduced chi-squares   ((Subscript[χ, (Subscript[ν, 1])])^2)/ ((Subscript[χ, (Subscript[ν, 2])])^2)), with degrees-of-freedom (Subscript[ν, 1]) (numerator) and (Subscript[⋁, 2]) (denominator).

p[f_,ν1_,ν2_]:=((Gamma[(ν1+ν2)/2])/(Gamma[ν1/2] Gamma[ν2/2])) (((ν1))^(ν1/2)) (((ν2))^(ν2/2)) ((f^((ν1/2)-1))/(((ν2+ν1 f))^((ν1+ν2)/2)))

Plot[p[f,1,10],{f,0,4}]

(∫_(.490)^∞)p[f,1,10]\[DifferentialD]f//N

fF = {.490,1.49,3.28,4.96,6.94,10.0,12.8,21.0}

Length[fF]

Here are f values

fvalues=Table[(∫_(fF[[i]])^∞)p[f,1,10]\[DifferentialD]f//N,{i,1,Length[fF]}]