If ∫ 1 2 d x x 2 - 2 x + 4 3 2 = k k + 5 , then k is equal to

Step-by-step solution

∫ 1 2 d x ( ( x − 1 ) 2 + 3 ) 3 2 Substituting x - 1 = 3 tan ⁡ θ ​ ⇒ d x = 3 sec 2 θ · d θ ​ Now ∫ 0 π 6 3 sec 2 θ​ ⁡ d θ​ 3 3 sec 3 θ​ = 1 3 ∫ 0 π 6 cos θ d θ ​ = 1 3 sin ⁡ θ 0 π 6 = 1 6 ⇒ 1 6 = k k + 5 = k + 5 = 6 k = k = 1 .