Mathematica: Evaluating integral

In summary, Niles is seeking assistance with an integral that cannot be solved in closed form using Mathematica. He has attached his notebook for reference and is hoping for feedback. The third integral appears to have no closed form solution, indicating that the original problem likely does not have one either.
  • #1
Niles
1,866
0
Hi

I need some assistance with the attached integral. I have tried performing it in Mathematica, but it doesn't give me the result in closed form. It just shows the integral.

I have attached my notebook if someone wants to test it out. I would be very happy to receive some feedback as I have spent many hours trying to make this work.


Niles.
 

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  • #2
It has successfully done the two inner integrals and fails on the final integral.

If I have not made a mistake then a substantially simplified version of your third integral is

Integrate[(vZ*Erf[vZ]^2)/E^vZ^2, {vZ, 0, Infinity}]

and there does not appear to be a closed form solution to that so I do not expect your actual problem has one either.
 
Last edited:
  • #3
Thanks, I believe you are right.Niles.
 

1. What is Mathematica?

Mathematica is a powerful and widely-used software program designed for mathematical computation, data analysis, and visualization. It is commonly used in scientific, engineering, and academic fields for tasks such as evaluating integrals, solving differential equations, and creating interactive visualizations.

2. How can Mathematica help with evaluating integrals?

Mathematica has a built-in function called Integrate which allows users to easily evaluate integrals symbolically. This means that Mathematica will provide an exact solution in terms of mathematical expressions, rather than just numerical approximations.

3. Can Mathematica also handle improper integrals?

Yes, Mathematica has the ability to evaluate improper integrals using the Integrate function. It can handle both infinite limits of integration and integrands with singularities, providing accurate results.

4. Are there any special techniques for evaluating integrals in Mathematica?

Yes, Mathematica has several built-in functions and techniques specifically designed for evaluating integrals. These include Integrate for symbolic integration, NIntegrate for numerical integration, and Integrate with specific methods for certain types of integrals, such as Integrate[expr, x, Assumptions -> x > 0] for definite integrals with positive limits.

5. How accurate are the results from evaluating integrals in Mathematica?

The accuracy of the results depends on the complexity of the integral and the chosen method of evaluation. For simple integrals, Mathematica can provide exact solutions. For more complex integrals, it may use numerical approximations which can be adjusted for desired precision. Users can also specify assumptions and constraints to improve the accuracy of the results.

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