Let [ t ] denote the greatest integer function. If ∫ 0 2 . 4 x 2 d x = α + β 2 + γ 3 + δ 5 , then α + β + γ + δ is equal to

Step-by-step solution

Given that ∫ 0 2 . 4 x 2 d x = α + β 2 + γ 3 + δ 5 , then  α + β + γ + δ We know that for 1 ≤ x < 2 ​, x = 1 ​​​​​​ ⇒ ∫ 0 2 . 4 x 2 d x = ∫ 0 1 0 d x + ∫ 1 2 1 d x + ∫ 2 3 2 d x + ∫ 3 2 3 d x + ∫ 2 5 4 d x + ∫ 5 2 . 4 5 d x = 0 + ( 2 - 1 ) + 2 ( 3 - 2 ) + 3 ( 2 - 3 ) + 4 ( 5 - 2 ) + 5 2 . 4 - 5 = 9 - 2 - 3 - 5 This is in the form of α + β 2 + γ 3 + δ 5 α = 9 ,   β = - 1 , &