If ∫ 20 40 sin ⁡ x sin ⁡ x + s i n 60 - x d x = k , then the value of k 4 is equal to

Step-by-step solution

As, k = ∫ 20 40 sin ⁡ x sin ⁡ x + s i n 60 - x d x .... (i) Applying a + b - x property, we get, k = ∫ 20 40 sin ⁡ 60 - x s i n 60 - x + sin ⁡ x d x ... (ii) Adding (i) and (ii), we get, 2 k = ∫ 20 40 1   d x = x 20 40 ⇒ 2 k = 40 - 20 ⇒ k = 10 ∴ k 4 = 2.5