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June 10th, 2019, 12:48 AM  #1 
Member Joined: Apr 2017 From: India Posts: 73 Thanks: 0  Two different answers through two different approaches
While evaluating this integral, I am getting different answers as I approach through different ways. Am I incorrect somewhere or is there any other explanation for such integrals?

June 10th, 2019, 05:41 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
What limits apply when you integrate with respect to x? What limits apply when you integrate with respect to y? 
June 10th, 2019, 09:06 AM  #3 
Member Joined: Apr 2017 From: India Posts: 73 Thanks: 0 
The limits for x are 0<x< y The limits for y are 0<y<infinity I tried to look up into what makes the answer different but was unable to figure out on my own. Please help me identify the mistake, if there is any. 
June 10th, 2019, 12:48 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
Your first way is correct. For your second way, the limits for y need to represent x < y < infinity. With that change, your second way produces 1/3, in agreement with the first way. 

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