Assume: b1>0, b2>0 and x>1

Define:

W(x)= int (sin(q)*(1-exp(-b1*abs(1-x*sin(q))))*(1+exp(-b2*abs(1-x*sin(q))))*sign(1-x*sin(q)), 0, 2*pi).

Prove that:

W(x)<W(1) for all x>1

Note 1: I've used "int(Y,a,b)" for definite intgration of Y from a to b.

Note 2: pdf version attached