Integral that MAPLE could not evaluate

In summary, the conversation discusses a problem with evaluating an integral involving an exponential function with a complex irrational trig function as the exponent. Attempts were made to transform the integral in hopes of finding a solution, but no luck. The integral is part of a solution for a radiation wave and resembles an elliptic integral. It is suggested that the integral may only be evaluated numerically for specific values.
  • #1
tsunamiBTP
4
0
I have attached a pdf of output from MAPLE attempting to evaluate an integral of an exponential function containing a complex irrational trig function as the exponent. MAPLE could not evaluate it when integrating with respect to the hangle phi. I then transformed the integral via varible substitutions to hopefully get it in a form that might be executable, but no luck there either.

Any suggestions?

This integral is a portion of a solution of a radiation wave emanating in the vicinity of source that is configured as a disc.
 

Attachments

  • integral output.pdf
    26.6 KB · Views: 331
Physics news on Phys.org
  • #2
That looks to me like a variation on an elliptic integral.
 
  • #3
There is no reason to think this integral has a closed form evaluation.
 
  • #4
Is g_edgar suggesting that this integral can only be evaluated numerically for specific values for r & theta?
 

1. Why can't MAPLE evaluate an integral?

MAPLE is a computer algebra system that uses algorithms and methods to solve mathematical problems, including integrals. However, not all integrals can be solved analytically, and MAPLE may not have the necessary algorithms to evaluate a particular integral. In such cases, MAPLE will return the integral in its original form without evaluating it.

2. Is there an alternative method to evaluate an integral that MAPLE cannot solve?

Yes, there are other computer algebra systems and software programs that may be able to solve the integral that MAPLE cannot. Additionally, numerical methods such as the trapezoidal rule or Simpson's rule can be used to approximate the value of the integral.

3. Can I change the settings or parameters in MAPLE to evaluate the integral?

In some cases, changing the settings or parameters in MAPLE may help in evaluating an integral. You can try adjusting the precision or using different methods, but there is no guarantee that this will work for every integral.

4. Does the inability of MAPLE to evaluate an integral mean it is unsolvable?

No, the fact that MAPLE cannot evaluate an integral does not necessarily mean it is unsolvable. It could mean that the integral is too complex or that MAPLE does not have the necessary algorithms to solve it. However, it is still possible that the integral can be solved using other methods or software.

5. How can I check if MAPLE has evaluated an integral correctly?

You can check the solution given by MAPLE by differentiating it. If the resulting expression is equivalent to the integrand, then MAPLE has evaluated the integral correctly. You can also try using different values for the variables to see if the solution remains the same, as this can also help verify the correctness of the evaluated integral.

Similar threads

A Orthogonality of variations in Faddev-Popov method for path integral
    • Quantum Physics
Replies
1
Views
638
Circular antenna array formula
    • Electrical Engineering
Replies
15
Views
2K
Attempting to Evaluate a Putnam Integral
    • Calculus and Beyond Homework Help
Replies
14
Views
2K
Maple BRS: Solving Killing/Geodesic Eqns with Maple's casesplit
    • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
2K
MHB Is this approach to evaluating a complex integral valid?
    • Topology and Analysis
Replies
2
Views
3K
Mathematica How to type mathematical equations using LaTeX
    • MATLAB, Maple, Mathematica, LaTeX
Replies
3
Views
275
Stat mech: probability density - 2 interacting particles
    • Advanced Physics Homework Help
Replies
4
Views
1K
Solving Difficult Integral: \int\frac{1}{1+x^7}dx
    • Calculus and Beyond Homework Help
Replies
10
Views
2K
Requesting suggestions for languages, libraries, and architectures for parallel (and sometimes non parallel) numerical and scientific computations
    • Programming and Computer Science
Replies
8
Views
2K
What is an effective variable substitution for solving this integral?
    • Calculus
Replies
11
Views
5K

Hot Threads

Recent Insights

Back
Top