Mathematica How Can I Solve Integration Problems in Mathematica?

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The discussion centers on a user encountering difficulties with numerical integration in Mathematica for a specific function related to electric fields and ionization. The user defines constants for electric field strength, ion concentration, permittivity, and charge. The integration involves calculating values between two derived limits, x1 and x2, which depend on these constants. However, an error message indicates issues with the integration variable or limits, suggesting that the input values may be too large or improperly formatted. The user expresses frustration with the software, noting that a previous version produced complex results. The conversation highlights challenges in numerical computation and the importance of correctly setting integration parameters in Mathematica.
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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:
Physics news on Phys.org
M. version 6.0.1.0 yields -3.85436*10^36 - 1.25626*10^44 \[ImaginaryI]
 

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