I saw this problem in another forum yesterday. Here's another solution:
Let Now let and the integral becomes let and the integral becomes let and the integral becomes
Now the limit becomes Finally, by Dominated Convergence Theorem the limit equals
Dominated convergence theorem!!
What is this Dominated convergence theorem? (The wiki article is greek to me, with "measure spaces" )
Can you,please, state the conditions and the theorem and illustrate an interesting example case where this theorem is powerful?