If ₀^ 3 2 ksec d =1- 1 2 ,(k 0) , then the value of k is

Step-by-step solution

aligned & Let I = ₀^ 3 2 k d & = 1 2 k ₀^ 3 d & = 1 2 k ₀^ 3 ~d aligned array ll & array l Let = t d =- dt array & when = 3 , t = 1 2 & when =0, t =1 & I= -1 2 k ₁^ 1 2 1 t dt & = -1 2 k . t ^ 1 2 ]₁^ 1 2 1 2 array = - 2 k ( 1 2 -1 )= 2 k (1- 1 2 ) Given that I= (1- 1 2 ) 2 k =1 k =2