# Integrate d/dx(x^2)

1. Feb 3, 2005

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

2. Feb 3, 2005

### Crosson

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. Feb 3, 2005

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

4. Feb 4, 2005

### Crosson

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. Feb 4, 2005

### HallsofIvy

Staff Emeritus
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:

$\int f(x)dx$, the indefinite integral should have an unknown constant added because it means ALL functions whose derivative is f(x) but $\int_a^xf(t)dt$ would not and the value will depend upon the choice of a.