What is an Integral Solution in Equations?

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In summary, an integral solution for an equation means that the solution is an integer and all the variables involved have their roots in the form of integers. This means that the solution will not involve decimals or fractions.
  • #1
teddyayalew
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I've seen the word used in a context that is not related to calculus, but I never understood what it meant. What does it mean if an equation has an integral solution?

Here is a context:If X^2 +Y^2 = 2aXY has a positive integral solution, find the value of a. What does it mean to have an integral solution?
 
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  • #2
It means that the solution is an integer.
 
  • #3
It means that all the variables involved have their roots in form of integers.
 
  • #4
As stated above, I believe that the solution is an interger (i.e. you won't have decimal or fractions as an answer).
 
  • #5
CallMeShady said:
As stated above, I believe that the solution is an interger (i.e. you won't have decimal or fractions as an answer).
That's integer, but you are otherwise correct.
 

1. What is the meaning of the word "integral" in math?

In math, an integral is a mathematical concept that represents the area under a curve on a graph. It is also used to calculate volumes and other quantities in higher dimensions.

2. Is the word "integral" used in any other fields besides math?

Yes, the word "integral" has various meanings in different fields. It can refer to something that is essential or necessary, or it can mean the entire whole or entirety of something. In physics, it is used to describe a fundamental part of a system, and in music, it refers to a harmonic relationship between notes.

3. What is the difference between definite and indefinite integrals?

A definite integral has specific limits of integration, meaning that the integration is performed over a specific range of values. On the other hand, an indefinite integral does not have limits and represents a general solution to an integration problem.

4. How is the concept of integral related to differentiation?

Integration and differentiation are known as inverse operations. Integration involves finding the antiderivative of a function, which is the original function that would result in the given derivative. In other words, integration "undoes" differentiation.

5. Can integrals be used in real-life applications?

Yes, integrals have many real-life applications, such as calculating distance, velocity, and acceleration in physics problems. They are also used in economics, engineering, and other fields to model and solve complex problems.

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