integrate d/dx(x^2)

by adamg
Tags: confused, d or dxx2, integrate
adamg is offline
Feb3-05, 04:35 PM
P: 48
if i integrate d/dx(x^2), should i include the constant of integration? thanks
Phys.Org News Partner Mathematics news on
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Crosson is offline
Feb3-05, 04:50 PM
P: 1,294
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.
adamg is offline
Feb3-05, 06:07 PM
P: 48
so it doesnt matter that you know what the function was before differentiation?

Crosson is offline
Feb4-05, 02:15 AM
P: 1,294

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).
HallsofIvy is online now
Feb4-05, 11:56 AM
Sci Advisor
PF Gold
P: 38,895
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.

Register to reply

Related Discussions
confused about SR Special & General Relativity 40
Confused at: du = f'(x) dx Calculus 13
confused Calculus & Beyond Homework 2
Confused Introductory Physics Homework 1
confused... Introductory Physics Homework 2