Question

Find the value of ∫log(a² cos² x + b² sin² x) dx for x ∈ [0,π/2].

Answer 1

Let

(Let k = b/a)

Where

 

(Let t = tan x)

Integrating, we get

I₁ = π log|k + 1| + c 

When k = 1, I₁ = 0, then c = –πlog 2

Thus, I₁ = π log |(1 + k)/2|

Therefore,