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June 10th, 2019, 12:48 AM   #1
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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?
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June 10th, 2019, 05:41 AM   #2
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What limits apply when you integrate with respect to x?

What limits apply when you integrate with respect to y?
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June 10th, 2019, 09:06 AM   #3
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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.
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June 10th, 2019, 12:48 PM   #4
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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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