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Integrate d/dx(x^2) 
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#1
Feb305, 04:35 PM

P: 48

if i integrate d/dx(x^2), should i include the constant of integration? thanks



#2
Feb305, 04:50 PM

P: 1,295

If you are working on an equation, then presumably you are integrating both sides with respect to x in which case you will have a constant of Integration (arbitrarily) on either side.
The short answer is yes, in all cases. 


#3
Feb305, 06:07 PM

P: 48

so it doesnt matter that you know what the function was before differentiation?



#4
Feb405, 02:15 AM

P: 1,295

Integrate d/dx(x^2)
I am tempted to say that it wouldn't matter, but that would lead to inconsistent results (i.e. a different answer depending on the chosen order of operations).



#5
Feb405, 11:56 AM

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P: 39,549

What in the world do you mean? If you start with a function f(x), differentiate it, then integrate that, whether you get the original function, that function plus an unknown constant, or that function plus a specific number depends on exactly what type of "integral" you are doing:
[itex]\int f(x)dx[/itex], the indefinite integral should have an unknown constant added because it means ALL functions whose derivative is f(x) but [itex]\int_a^xf(t)dt[/itex] would not and the value will depend upon the choice of a. 


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