- #1
Two solutions for same problem dont match ?
- Thread starter Miike012
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SUMMARY
The forum discussion addresses the integration of two expressions, specifically comparing the results of integrating the function involving natural logarithms. The two solutions presented are x - 6 + 6ln(x - 6) + C and x + 6ln(x - 6) + C. It is concluded that both expressions are equivalent, as the difference in constants (C and C-6) does not affect the validity of the solutions. The discussion emphasizes the importance of recognizing arbitrary constants in integration.
PREREQUISITES- Understanding of integration techniques in calculus
- Familiarity with natural logarithms and their properties
- Knowledge of arbitrary constants in mathematical expressions
- Basic algebraic manipulation skills
- Study the properties of arbitrary constants in integration
- Learn more about integration techniques involving logarithmic functions
- Explore the concept of equivalence in mathematical expressions
- Review calculus fundamentals, particularly integration and differentiation
Students, educators, and professionals in mathematics or engineering who are working with integration and logarithmic functions will benefit from this discussion.
- #2
tiny-tim
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Hii Miike012! 
Your two solutions are
They're the same!
(different C
)
Your two solutions are
x - 6 + 6ln(x - 6) + C
and x + 6ln(x - 6) + C
and x + 6ln(x - 6) + C
They're the same!
(different C
)- #3
awkward
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Your answers are the same.
If C is an arbitrary constant, then C-6 is also an arbitrary constant.
(Beaten to the punch by tiny-tim.)
If C is an arbitrary constant, then C-6 is also an arbitrary constant.
(Beaten to the punch by tiny-tim.)
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