Integration Constant in Physics: When to Use It?

[gracy]

I have not taken maths so you may find my question silly. in physics i have to deal with integration.so can you please tell me where we write integration constant and where we don't?

 

[Vrbic]

If you are solving some generic problem by integration, you put integration constant everywhere it belong to. But when you are dealing with an exact situation, you have to put for example start position, and from this information you determine your constant and you exchange the constant by exact value. Many times this initial value is defined for convenience in that way that constant is equal "0" or "1" and you can not notice a presence of it.

For example: if you want to find out velocity v(t) (dependent on time t) from acceleration (gravitational), you integrate $\int g dt =gt + v_0$, where $v_0$ is integration constant. But it is common to start that you drop stone or something (no throw). If you just let it fall initial velocity $v_0=0$. And you see formula v=gt.

 

[MarneMath]

The short answer is - You use a constant of integration when you evaluate an indefinite integral. The constant of integration is not needed (or canceled out) whenever you use a definite integral.

 

[Vrbic]

The short answer is - You use a constant of integration when you evaluate an indefinite integral. The constant of integration is not needed (or canceled out) whenever you use a definite integral.

Easier view :)
In the language of my example: You are interested in change of velocity between t1=0s and t2=1s. Than you integrate from 0 to 1.

 

[gracy]

The short answer is - You use a constant of integration when you evaluate an indefinite integral. The constant of integration is not needed (or canceled out) whenever you use a definite integral.

OK.
K is integral constant. in indefinite integral We might have some information elsewhere in the problem that will help us to find this constant.My question is which kind of information would be given in the question so that i can figure out it should be K.

 

[Mark44]

OK.
K is integral constant. in indefinite integral We might have some information elsewhere in the problem that will help us to find this constant.My question is which kind of information would be given in the question so that i can figure out it should be K.

It should be reasonably straightforward to determine whether the problem is asking for a definite integral or an indefinite integral.

In problems like the one in your OP, they will usually state initial conditions, such as the initial velocity and initial position.

 

[HallsofIvy]

That typically involves understanding the problem, and what your variables mean in terms of the problem, more than the mathematics used to solve the problem.