Integration using partial fractions

jpanknin

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Jan 8, 2020
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Hi everyone, I have a question related to the screenshot below. In the second to last series of equations at the bottom of the image, the author chose A/(x-1) and B/(x+2). Is there a reason for this order? Why not A/(x+2) and B/(x-1)? (x+2) and (x-1) both have degree 1, so why are they not interchangeable for A and B? And more generally, is there a precedence of order for the factors of the denominator?


A03FF03A-00F0-4C97-A635-5CE9C7E49942_1_105_c.jpeg
 

Dr.Peterson

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Nov 12, 2017
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Hi everyone, I have a question related to the screenshot below. In the second to last series of equations at the bottom of the image, the author chose A/(x-1) and B/(x+2). Is there a reason for this order? Why not A/(x+2) and B/(x-1)? (x+2) and (x-1) both have degree 1, so why are they not interchangeable for A and B? And more generally, is there a precedence of order for the factors of the denominator?
Why would you think order would matter at all? It doesn't. And which constant you call A has no effect on any of the work that follows.

In other words, they are entirely interchangeable. You can do as you wish.
 

Jomo

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Personally I would use r and s for the constants. Do you think that the solution would change.
 

Subhotosh Khan

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Hi everyone, I have a question related to the screenshot below. In the second to last series of equations at the bottom of the image, the author chose A/(x-1) and B/(x+2). Is there a reason for this order? Why not A/(x+2) and B/(x-1)? (x+2) and (x-1) both have degree 1, so why are they not interchangeable for A and B? And more generally, is there a precedence of order for the factors of the denominator?


View attachment 29193
Have you tried switching A & B? What answer do you get?

You should find that the final answer does not depend on that action.
 
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