Register to reply

Importance of adding the constant of integration.

by shayaan_musta
Tags: adding, constant, importance, integration
Share this thread:
shayaan_musta
#1
Oct10-11, 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.
Phys.Org News Partner Science news on Phys.org
Physical constant is constant even in strong gravitational fields
Montreal VR headset team turns to crowdfunding for Totem
Researchers study vital 'on/off switches' that control when bacteria turn deadly
daveb
#2
Oct10-11, 08:26 AM
P: 925
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.
dextercioby
#3
Oct10-11, 09:26 AM
Sci Advisor
HW Helper
P: 11,956
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 ?

shayaan_musta
#4
Oct11-11, 09:05 AM
P: 184
Importance of adding the constant of integration.

Quote Quote by dextercioby View Post
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 ?
f(x)=[itex]\frac{x^{5}}{5}[/itex] + [itex]\frac{5x^{2}}{2}[/itex] + c

where "c" is the integration constant.

Now what?? :s
shayaan_musta
#5
Oct11-11, 09:08 AM
P: 184
Quote Quote by daveb View Post
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.
Ok daveb thank you. I think you have answered my question.
Thank you very much.
shayaan_musta
#6
Oct11-11, 09:09 AM
P: 184
Thank you dextercioby. You also made me to think the answer of my question.
cpt_carrot
#7
Oct11-11, 10:59 AM
P: 24
Quote Quote by shayaan_musta View Post
f(x)=[itex]\frac{x^{5}}{5}[/itex] + [itex]\frac{5x^{2}}{2}[/itex] + c

where "c" is the integration constant.

Now what?? :s
Not quite, this is why the constant of integration is important. The first integration gives

[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
HallsofIvy
#8
Oct11-11, 02:22 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,691
Note that dextercioby's example is a linear second order non-homogenous differential equation which means that the set of all solutions is a two dimensional "linear manifold". That is why you need two undetermined coefficients.
shayaan_musta
#9
Oct12-11, 01:55 AM
P: 184
Quote Quote by cpt_carrot View Post
Not quite, this is why the constant of integration is important. The first integration gives

[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
Ok cpt_carrot I got you. Thanks man.
Now I have understood that for each integration a constant is important, as Hallsofivy said.

So help guys on Physics Forums


Register to reply

Related Discussions
Thermo physics. Dealing with adding dQ to a system with P held constant. Advanced Physics Homework 4
Monte Carlo Integration - Importance Sampling General Math 1
Simple Spring Constant Lab...not adding up Introductory Physics Homework 7
Adding buoyancy to 3D integration of diffusion equation Introductory Physics Homework 0
Adding a constant V to the wave equation Introductory Physics Homework 21