Integration Constant in Physics: When to Use It?

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Discussion Overview

The discussion revolves around the use of integration constants in physics, particularly in the context of indefinite versus definite integrals. Participants explore when and why integration constants are applied in various scenarios, including the importance of initial conditions in determining these constants.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested, Homework-related

Main Points Raised

  • One participant questions the necessity of integration constants in physics, seeking clarification on their application.
  • Another participant explains that integration constants are used in indefinite integrals and can be determined from initial conditions in specific problems.
  • Several participants emphasize that definite integrals do not require an integration constant, as they are canceled out in the evaluation process.
  • There is a discussion about how initial conditions, such as initial velocity or position, are typically provided in problems to help determine the integration constant.
  • One participant notes that understanding the problem context and the meaning of variables is crucial for determining the need for an integration constant.

Areas of Agreement / Disagreement

Participants generally agree on the distinction between indefinite and definite integrals regarding the use of integration constants. However, there is some uncertainty about the specific types of information needed to determine the integration constant in various problems.

Contextual Notes

Limitations in the discussion include a lack of detailed examples illustrating the application of integration constants and the potential ambiguity in problem statements that may affect the determination of these constants.

Who May Find This Useful

This discussion may be useful for students and individuals learning about integration in physics, particularly those seeking to understand the role of integration constants in different types of integrals.

gracy
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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?
 
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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.
 
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.
 
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MarneMath said:
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.
 
MarneMath said:
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.
 
gracy said:
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.
 
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.
 

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