Problem Finding Integral equation for 2*Cos( a*x) *Cos(b/x)

In summary, the conversation discusses the difficulties in creating an integral equation for Integral 2 * Cos(a*x) * Cos(b/x) dx. The only potential solution mentioned is to expand the equation in powers of x.
  • #1
CAP71
2
0
Hi

I'm struggling to create an integral equation for

Integral 2 * Cos( a*x) *Cos(b/x) dx

Has anybody seen a potential solution for this. Mathematica online can solve each part individually however it is unable to create the integral for the entire equation.

Thanks
 
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  • #2
Welcome to PF!

CAP71 said:
Integral 2 * Cos( a*x) *Cos(b/x) dx

Hi CAP71! Welcome to PF! :smile:

(have an integral: ∫ :wink:)

Apart from writing it cos(a*x + b/x) + cos(a*x - b/x) and then maybe expanding it in powers of x, I don't see anything. :blushing:
 
  • #3
Thankyou Tiny-Tim for your response. I will look further into using the expanding powers method. I didn't think there was going to be a straight foward integral equation however I was trying to be optomistic.
 

FAQ: Problem Finding Integral equation for 2*Cos( a*x) *Cos(b/x)

1. What is an integral equation?

An integral equation is a mathematical equation that contains an unknown function within an integral sign. It is used to solve problems in which the solution is dependent on the entire function rather than just a specific value.

2. How do you find the integral equation for 2*Cos(a*x)*Cos(b/x)?

To find the integral equation for this function, we first need to use the trigonometric identity cos(a)*cos(b) = (1/2)*(cos(a+b) + cos(a-b)). Then, we can rewrite the original function as 2*Cos(a*x)*Cos(b/x) = Cos(a*x + b/x) + Cos(a*x - b/x). Finally, we can integrate each term separately to get the integral equation.

3. What is the purpose of finding the integral equation for a function?

The integral equation allows us to solve for the unknown function in a more general and comprehensive way. It can also help us to understand the behavior of the function and make predictions about its values for different inputs.

4. Are there any specific techniques or methods for finding integral equations?

Yes, there are various techniques and methods for finding integral equations depending on the type of function. Some common techniques include using trigonometric identities, integration by parts, and substitution.

5. Can integral equations be used in real-life applications?

Yes, integral equations have many practical applications in fields such as physics, engineering, and economics. They can be used to model and solve complex problems in these areas, such as predicting the behavior of a physical system or optimizing a financial decision.

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