If the value of the integral Ι = ∫ π 4 π 3 m a x sin x , tan ⁡ x d x is equal to ln ⁡ k , then the value of k 2 is equal to

Step-by-step solution

For x ∈ π 4 , π 3 ,   tan ⁡ x > sin ⁡ x (as cos ⁡ x < 1 ) ∴ m a x tan ⁡ x , sin ⁡ x = tan ⁡ x Thus, Ι = ∫ π 4 π 3 tan ⁡ x d x = - ln ⁡ cos ⁡ x π 4 π 3 = - ln ⁡ 1 2 + ln ⁡ 1 2 = ln ⁡ 2