The value of ∫ 0 π / 2 s g n sin 2 ⁡ x - sin ⁡ x + 1 2 d x is equal to, (where, s g n x denotes the signum function of x )

Step-by-step solution

⇒ sin 2 ⁡ x - sin ⁡ x + 1 2 = sin ⁡ x - 1 2 2 + 1 4 > 0  ∀ x ∈ 0 , π 2 ∴   s g n sin 2 ⁡ x - sin ⁡ x + 1 2 = 1 Thus, Ι = ∫ 0 π 2 1 d x = x 0 π 2 = π 2