How Can I Solve Integration Problems in Mathematica?

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SUMMARY

The discussion focuses on solving integration problems in Mathematica, specifically using version 6.0.1.0. The user encounters an error when attempting to numerically integrate a function involving physical constants such as efield, ion, and \[Epsilon]. The integration limits x1 and x2 are defined based on these constants, but the user receives an "Invalid integration variable or limit(s)" error message. The integration expression involves complex calculations that result in imaginary components, indicating potential issues with the input parameters or the integration method.

PREREQUISITES
  • Understanding of numerical integration in Mathematica
  • Familiarity with physical constants and their significance in calculations
  • Knowledge of error handling in Mathematica
  • Basic proficiency in defining functions and variables in Mathematica
NEXT STEPS
  • Review Mathematica's documentation on numerical integration functions
  • Learn how to troubleshoot integration errors in Mathematica
  • Explore the use of complex numbers in Mathematica calculations
  • Investigate the implications of physical constants in numerical simulations
USEFUL FOR

Mathematica users, physicists, and engineers dealing with numerical integration and seeking to resolve integration errors in their computations.

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Homework Statement



I'm having problems interating the following function numerically using Mathematica.
efield := 10^15
ion := 10^-15
\[Epsilon] := 8.8541878176^-12
q:=1.60217648710^-19

Homework Equations




x2:= (1/2 - 1/(2*ion) Sqrt[ion^2 - (q^3*efield^2)/(\[Pi]*\[Epsilon])])
x1:= (1/2 + 1/(2*ion) Sqrt[ion^2 - (q^3*efield^2)/(\[Pi]*\[Epsilon])])
Integrate[(3/2)*
Sqrt[1 - q^3*
efield*x^(-1)/(4*\[Pi]*\[Epsilon]) - x], {x,
x1, x2}]


The Attempt at a Solution


I receive the following error message:
Integrate::ilim: "Invalid integration variable or limit(s) in \
{1000000000000000000000000000000\ 1.60218^(19\\:2212)\ \
x,1/2-500<<8>>0000\ <<1>>,1/2+500000000000000 \
Sqrt[1/(100<<25>>000)-<<1>>]}"

I hate computers
 
Last edited:
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M. version 6.0.1.0 yields -3.85436*10^36 - 1.25626*10^44 \[ImaginaryI]
 

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