Cases in which constants can absorb terms

In summary, constants of integration can be absorbed and redefined as c in cases where c is any constant, including zero, and c can be raised to a power or be a trigonometric function. However, for cases where the constant is in the denominator or involves specific domains, such as C = 0 or C > 0, separate considerations must be made.
  • #1
Duderonimous
63
1

Homework Statement



What are the cases in which constants of integration can and cannot absorb terms and operations and just be redefined as c.


Homework Equations





The Attempt at a Solution



As long as I keep redefining my constant of integration I can say

-c=k

ac=k where in any constant including zero

c^(a)=k

Can I say
1/c=k?
ln|c|=k?
sin(c)=k (or any trig function for that matter)

or for these last examples do I need to define the domain of c
 
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  • #2
Hi Duderonimous! :smile:
Duderonimous said:
… or for these last examples do I need to define the domain of c

Yes.

But it's usually fairly obvious what you can do.

eg, if it's + 1/C, then obviously C = 0 is a problem that you'll have to deal with separately :wink:

(and you'll probably have to deal with C > 0 and C < 0 separately also)
 

FAQ: Cases in which constants can absorb terms

What are constants in scientific equations?

Constants in scientific equations are numerical values that do not change and remain the same throughout the equation. They are typically represented by letters such as "k" or "c".

How do constants affect the results of scientific calculations?

Constants can either amplify or diminish the impact of other terms in an equation. They can also determine the overall behavior or trend of the equation. For example, a larger constant in a physics equation may indicate a stronger force or a higher value in a chemical equation may result in a faster reaction.

Can constants absorb other terms in an equation?

Yes, constants can absorb other terms in an equation when they are multiplied or divided together. For example, in the equation y = kx, the constant "k" can absorb the variable "x" when multiplied together, resulting in a new constant value for the equation.

How does changing the value of a constant affect the equation?

Changing the value of a constant can significantly alter the results of the equation. A larger constant value can lead to a larger overall result, while a smaller constant value can result in a smaller overall result.

Are there specific cases in which constants can absorb terms?

There are various cases in which constants can absorb terms in different scientific fields. For instance, in thermodynamics, the ideal gas law equation (PV = nRT) has a constant "R" that can absorb the terms for pressure (P), volume (V), and temperature (T). In kinematics, the equation v = v0 + at has a constant "a" that can absorb the terms for initial velocity (v0) and time (t).

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