(by the way, you wrote instead of )
And in order to do this problem, you have to assume that the three rv's are independent.
Your integral is that of so this is not what you want.
In order to find the probability you're looking for, you need to integrate the joint pdf of the three rv's over the region where
So this gives
So this gives you a new boundary for the integral with respect to ... continue and you will find the answer