Please explain this step

Ankit006

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This is one of the double integral math examples in my textbook. I don't understand this step. How we can move dy like this. isn't integral 0 to 1 for dx. (Sorry for my bad english)
Screenshot 2022-08-06 005601.png
 

Dr.Peterson

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This is one of the double integral math examples in my textbook. I don't understand this step. How we can move dy like this. isn't integral 0 to 1 for dx. (Sorry for my bad english)
View attachment 33595
I would say that the first integral is written incorrectly, as the order of dydx implies that the inner integral is with respect to y, which would make no sense. But possibly your book uses a different convention.

Can you show us the context? What is said before this may be important for clarification.
 

Ankit006

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I would say that the first integral is written incorrectly, as the order of dydx implies that the inner integral is with respect to y, which would make no sense. But possibly your book uses a different convention.

Can you show us the context? What is said before this may be important for clarification.
Screenshot 2022-08-06 090522.png
 

Ankit006

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It looks like we need more context! What has been said before this example? How have they defined the notation? What book is this from?
This problem is from a math pdf file my college give me. This problem is from the multivariable calculus chapter and the section is double and triple integral.
 

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Dr.Peterson

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This problem is from a math pdf file my college give me. This problem is from the multivariable calculus chapter and the section is double and triple integral.
This just shows that they are introducing the idea of dA = dxdy = dydx, but not how the order relates to the limits of integration. Presumably that is shown somewhere between the two things you've shown.

Ultimately, though, I think they just made a mistake in the problem you asked about. This isn't some advanced, specialized notation.
 
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