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) 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) (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