If [ ] denotes the greatest integer function, then ₀^ /3 [ x] ,dx =

Step-by-step solution

The given integral is I = ₀^ /3 [ x] , dx . In the interval [0, /3] , the function x is strictly increasing. For 0 x For /4 x /3 , 1 x 3 Splitting the integral at x = /4 , we get: I = ₀^ /4 0 , dx + _ /4 ^ /3 1 , dx I = 0 + [x]_ /4 ^ /3 I = 3 - 4 = 12 . Answer: 12