If the integral I = ∫ 2 x 2 4 + x 2 d x = 2 x - f x + c , where f 2 = π , then the minimum value of y = f x   ∀ x ∈ - 2,2 is (where, c is the constant of integration)

Step-by-step solution

I = 2 ∫ x 2 + 4 - 4 x 2 + 4 d x = 2 ∫ 1 - 4 x 2 + 4 d x = 2 x - 4 2 tan - 1 ⁡ x 2 + c = 2 x - 4 tan - 1 ⁡ x 2 + c ∴ f x = 4 tan - 1 ⁡ x 2 So, min ⁡ f x = 4 tan - 1 ⁡ - 1 = - π