The integral I = ∫ 0 100 π t a n - 1 x d x , (where, . represents the greatest integer function) has the value K π + tan ⁡ p , then the value of K + p is equal to

Step-by-step solution

The given integral is I = ∫ 0 tan 1 ⁡ 0 d x + ∫ tan ⁡ 1 100 π ⁡ 1 d x a s   tan - 1 x ⁡ ∈ 1 , π 2 ,   ∀ x > tan ⁡ 1 ⇒ I = 100 π - tan ⁡ 1 = 100 π + tan ⁡ - 1 ∴ k = 100 ,   p = - 1 ∴ k + p = 99