If ∆ x = f x + f ( - x ) 0 x 4 3 f x - f ( - x ) cos ⁡ x x 4 2 x f x f ( - x ) (where f ( x ) is a real valued function of x ) , then the value of ∫ - 2 2 x 4 ∆ ( x )

Step-by-step solution

∆ - x = f - x + f ( x ) 0 x 4 3 f - x - f ( x ) cos ⁡ x x 4 - 2 x f - x f ( x ) f x + f ( - x ) 0 x 4 3 f x - f ( - x ) cos ⁡ x x 4 - 2 x f x f ( - x ) = - ∆ ( x ) So, ∆ ( x ) is an odd function. ⇒ x 4 ∆ ( x ) is an odd function ⇒ ∫ - 2 2 x 4 ∆ x d x = 0