The value of the intgral∫π/2−π/2log(a−sinθa+sinθ)dθ, a>0 is?
I=∫π/2−π/2log(a−sinθa+sinθ)dθ
Putting θ=−θ, in the above equation, we get
I=∫π/2−π/2log(a+sinθa−sinθ)dθ
Thus, adding the above two equations, we get
2I=∫π/2−π/2log(1)dθ
I=0.