I'm not sure I would view it that way. How about this:
It depends on how you interpret the operator It's a multiplicative inverse, right? How is the original problem stated, exactly?
I have two ways here:
First Way: integrate x then calculate 1/(D-1) for the result (wich is x^2/2)
Second Way: evaluate 1/(D-1) for x then integrate the result
The problem here is that the two ways gives different results!
first way gives:
second way gives:
Anyone know a good site contains practice problems in inverse differential operator??
You are wasting my time.
Do not reply in this thread If you have no idea about the differential operators and thier inverses. I posted this thread to find someone help to fix my problem.
I did not post it to explain differential operators and thier inverses.
You are perilously close to breaking rules 3 and 11. If someone who is helping you asks for clarification, you are supposed to give it.
Since you bring up wasting time, I could just as easily claim you are wasting my time by being unclear in the OP. I've never seen anyone write the operational inverse of an operator as It is always for the very reason that it would be confusing otherwise.
Without knowing more, I'd say it would be safest to apply the first, because operators don't always commute (in fact, they rarely do). Without knowing how you're defining relative to I don't know whether they would commute. However, the expression
would definitely have you evaluating , followed by integrating.