The value of the integral ∫ 4 10 x 2 x 2 − 28 x + 196 + x 2 d x , where x denotes the greatest integer less than or equal to x , is

Step-by-step solution

Let I =   ∫ 4 10 x 2 x 2 - 28 x + 196 + x 2 d x ⇒ I =   ∫ 4 10 x 2 14 - x 2 + x 2   d x       . . . i Use ∫ a b f x d x = ∫ a b f a + b - x d x I =   ∫ 4 10 14 - x 2 x 2 + 14 - x 2   d x       . . . ii By adding equations i   &   ii , we get 2 I =   ∫ 4 10 14 - x 2 + x 2 x 2 + 14 - x 2   d x ⇒ 2 I =   ∫ 4 10 d x ⇒ 2 I = 6   ⇒ I = 3