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

Question

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, 101, 99, 100 π, 99 π

MARKS App · Accepted Answer

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

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