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Importance of adding the constant of integration. 
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#1
Oct1011, 07:36 AM

P: 184

Hello experts!
I have a question below. Why is it important to add the constant of integration immediately when the integration is performed? Thanks in advance. 


#2
Oct1011, 08:26 AM

P: 926

If you're wondering why there is a constant of integration, it is because when you have a function f(x) such that F(x) = f'(x), then the derivative of g(x) = f(x) + C for any constant also equals F(x) (i.e., g'(x) = f'(x)), so when you integrate F(x), you need to capture that constant in the solution.
Now, if you are asking why it has to be done immediately I'm not sure what you're asking since adding the constant is done as the last step. 


#3
Oct1011, 09:26 AM

Sci Advisor
HW Helper
P: 11,896

To the OP: Assume you must do a double integration. For example:
[tex] \frac{d^2 f(x)}{d x^2} = x^3 + 5 [/tex] What is then f(x) equal to ? 


#4
Oct1111, 09:05 AM

P: 184

Importance of adding the constant of integration.
where "c" is the integration constant. Now what?? :s 


#5
Oct1111, 09:08 AM

P: 184

Thank you very much. 


#6
Oct1111, 09:09 AM

P: 184

Thank you dextercioby. You also made me to think the answer of my question.



#7
Oct1111, 10:59 AM

P: 24

[tex] \frac{df}{dx}=\frac{x^4}{4}+5x+c_1 [/tex] and the second integration gives [tex] f(x)=\frac{x^5}{20}+\frac{5x^2}{2}+c_1x+c_2 [/tex] Which is why we need one constant of integration for each integral 


#8
Oct1111, 02:22 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,345

Note that dextercioby's example is a linear second order nonhomogenous differential equation which means that the set of all solutions is a two dimensional "linear manifold". That is why you need two undetermined coefficients.



#9
Oct1211, 01:55 AM

P: 184

Now I have understood that for each integration a constant is important, as Hallsofivy said. So help guys on Physics Forums 


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