Solving Integration Problem in Mathematica 6 for Beginners

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SUMMARY

The discussion centers on a user's difficulty with performing an integration in Mathematica 6, specifically the expression Integrate[exp[-k*z]*BesselJ[0, k*a]* BesselJ[1, k*a], {k, 0, Infinity}], which returns the original expression instead of a solution. The user notes that a simpler integration, Integrate[Sin[k], {k, 0, 1}], works correctly. A key resolution provided is the correction of the exponential function syntax from exp[x] to Exp[x].

PREREQUISITES
  • Basic understanding of Mathematica 6 syntax
  • Familiarity with Bessel functions
  • Knowledge of integration techniques in calculus
  • Understanding of exponential functions in programming
NEXT STEPS
  • Research proper syntax for functions in Mathematica 6, focusing on exponential functions
  • Explore advanced integration techniques in Mathematica, including handling special functions
  • Study Bessel functions and their applications in mathematical problems
  • Learn about debugging common errors in Mathematica code
USEFUL FOR

This discussion is beneficial for beginners in Mathematica, particularly those encountering integration challenges, as well as educators and students dealing with Bessel functions and exponential expressions in mathematical computations.

shehry1
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A beginner to Mathematica's question:

I try to make the following integration in mathematica 6 and I get back the same expression with the integration symbol next to it. Why?
Integrate[exp[-k*z]*BesselJ[0, k*a]* BesselJ[1, k*a], {k, 0, Infinity}]

Integrate[Sin[k], {k, 0, 1}] however gives the correct answer.

Not that it matters, the equation comes in one of Jackson's problems and I have seen solutions on the net that seem to make a jump to the solution saying 'using Mathematica...'
 
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shehry1 said:
A beginner to Mathematica's question:

I try to make the following integration in mathematica 6 and I get back the same expression with the integration symbol next to it. Why?
Integrate[exp[-k*z]*BesselJ[0, k*a]* BesselJ[1, k*a], {k, 0, Infinity}]

Integrate[Sin[k], {k, 0, 1}] however gives the correct answer.

Not that it matters, the equation comes in one of Jackson's problems and I have seen solutions on the net that seem to make a jump to the solution saying 'using Mathematica...'

Try correcting the expression. In particular, the Mathematica command for e^x is

Code:
Exp[x]

and not

Code:
exp[x]
 
eureka
 

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