∫ π 18 4 π 9 2 s i n x s i n x + c o s x d x = …

Step-by-step solution

Let = l ∫ π 18 4 π 9 2 s i n x s i n x + c o s x d x = 2 ∫ π 18 4 π 9 s i n x s i n x + c o s x d x …(i) = 2 ∫ π 18 4 π 9 sin ⁡ 4 π 9 + π 18 - x sin ⁡ 4 π 9 + π 8 - x + cos ⁡ 4 π 9 + π 8 - x d x ∵ ∫ a b f x d x = ∫ a b f a + b - x d x ⇒ l = 2 ∫ π 18 4 π 9 c o s x c o s x + s i n x d x …(ii) On adding Eqs. (i) and (ii), we get 2 l = 2 ∫ π 18 4 π 9 d x = 2 x π 18 4 π 9 = 2 4 π 9 - π 18 = 2 7 π 18 ⇒ l = 7 π 18