Find constants that satisfy integrals?

Also, what are the functions y1(x) and y2(x)? Are they related in any way? Some context needs to be provided in order to understand the question.In summary, the conversation discusses two definite integrals, ∫y1(x)^2dx and ∫y2(x)^2dx, from -∞ to +∞, both of which equal 1. The poster has evaluated the integrals and found that c1 is equal to c2, but they are unsure if this is correct. More information is needed, such as the functions y1(x) and y2(x) and their relationship to each other, to fully understand the question.
  • #1
sheldonrocks97
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Homework Statement


∫y1(x)^2dx from - to + infinity=1 and ∫y2(x)^2dx from - to + infinity=1

Homework Equations


None that I know of.

The Attempt at a Solution


I evaluated the integrals and got that c1 is equal to c2 but I think that's wrong.
 
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  • #2
sheldonrocks97 said:

Homework Statement


∫y1(x)^2dx from - to + infinity=1 and ∫y2(x)^2dx from - to + infinity=1

Homework Equations


None that I know of.

The Attempt at a Solution


I evaluated the integrals and got that c1 is equal to c2 but I think that's wrong.

Can you please show your detailed work? It's hard to understand the question. And you are required to show your work on schoolwork questions. Thanks.
 
  • #3
sheldonrocks97 said:

Homework Statement


∫y1(x)^2dx from - to + infinity=1 and ∫y2(x)^2dx from - to + infinity=1

Homework Equations


None that I know of.

The Attempt at a Solution


I evaluated the integrals and got that c1 is equal to c2 but I think that's wrong.
Your problem statement is very sketchy. What constants are you talking about? Both integrals appear to be definite integrals, so the constant of integration isn't relevant in either one.
 

FAQ: Find constants that satisfy integrals?

1. How do I find constants that satisfy integrals?

There are a few different methods for finding constants that satisfy integrals, but one common approach is to use the Fundamental Theorem of Calculus. This theorem states that if a function f(x) has an antiderivative F(x), then the definite integral of f(x) from a to b is equal to F(b) - F(a). By setting this equal to a given value and solving for the constant, you can find the value that satisfies the integral.

2. Can I use numerical methods to find constants that satisfy integrals?

Yes, numerical methods such as the trapezoidal rule or Simpson's rule can be used to approximate the value of a definite integral. However, these methods may not always be accurate and may require more computation than using the Fundamental Theorem of Calculus.

3. Do I need to know the exact form of the function to find constants that satisfy integrals?

No, in some cases you may be able to use techniques such as integration by parts or substitution to find the antiderivative of a function without knowing its exact form. However, in other cases, it may be necessary to know the function in order to find the constants that satisfy the integral.

4. Can I use a calculator or computer program to find constants that satisfy integrals?

Yes, many calculators and computer programs have built-in functions for finding integrals. However, it is important to double-check the results as these methods may not always be accurate.

5. Are there any common mistakes to avoid when finding constants that satisfy integrals?

One common mistake is forgetting to add the constant of integration when solving for the constant. Another mistake is using the wrong limits of integration, which can lead to incorrect results. It is also important to double-check your work and make sure all calculations are accurate.

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