Simplification of Integration Problem

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In summary, the conversation discusses the problem of simplifying an integral with two different functions, f(theta,phi) and g(theta,phi), being integrated with respect to phi. The question is whether the integrals can be combined or if they should be done separately and then divided at the end. The response explains that in general, the integrals cannot be combined and gives an example to illustrate this.
  • #1
mea03wjb
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Hi,

I have a problem with an integral - I'd like to simplify it as much as possible...


[tex] y =[/tex][tex]\int\frac{1}{f(theta,phi) }d.phi / \int\frac{1}{g(theta,phi)} d.phi[/tex]


2 different functions integrated with respect to phi. Note the division symbol between the integrals!

The limits of the integrals are the same so can I just put them in the same integration? Or should I do the integrations separately then divide the end result?

Thanks!
 
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  • #2
You most certainly cannot (in general) put them into the same integral. Test it out with a simple case. f(x) = x, g(x) = x. Then int(f)/int(g) = 1, but int(f/g) = int(1) = x.
 

FAQ: Simplification of Integration Problem

What is the purpose of simplifying an integration problem?

Simplifying an integration problem allows us to find a more concise and manageable solution. It also helps us to better understand the underlying concepts and relationships involved in the problem.

What are some common techniques used for simplifying integration problems?

Some common techniques include substitution, integration by parts, and using trigonometric identities. It is important to carefully choose the most appropriate technique for each problem.

Can simplifying an integration problem change the result?

Yes, simplifying an integration problem can change the result. This is because different techniques may lead to different solutions. It is important to check the answer obtained after simplification to ensure its accuracy.

How can I check if my simplified integration problem is correct?

One way to check if a simplified integration problem is correct is to differentiate the solution and see if it matches the original integrand. Another way is to use an online calculator or computer software to verify the answer.

Are there any tips for simplifying integration problems more efficiently?

One tip is to carefully evaluate the integral and identify any patterns or relationships that can be used to simplify the problem. It is also helpful to have a good understanding of basic integration rules and techniques. Practicing regularly and seeking help when needed can also improve efficiency in simplifying integration problems.

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