- #1
sportlover36
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how can i find a power series for this integral? [tex]\int cos(x^3)[/tex]
How can i find a power series for this integral?
- Thread starter sportlover36
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- Integral Power Power series Series
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SUMMARY
The discussion focuses on finding a power series for the integral of cos(x^3), specifically the integral ∫ cos(x^3) dx. The recommended approach is to utilize the known power series expansion for cos(x) and substitute x^3 in place of x. This method effectively transforms the integral into a series representation, allowing for easier computation and analysis.
PREREQUISITES- Understanding of power series expansions
- Familiarity with the integral calculus
- Knowledge of the cosine function's Taylor series
- Basic algebraic manipulation skills
- Study the Taylor series expansion for cos(x)
- Learn how to substitute variables in power series
- Explore techniques for integrating power series
- Investigate convergence criteria for power series
Students and educators in mathematics, particularly those studying calculus and series expansions, as well as anyone interested in advanced integration techniques.
- #2
tiny-tim
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Hi sportlover36! 
(have an integral: ∫ and a sigma: ∑ and try using the X2 tag just above the Reply box
)
Just write out the series for cosx, and then write x3 everywhere instead of x.
(have an integral: ∫ and a sigma: ∑ and try using the X2 tag just above the Reply box
)Just write out the series for cosx, and then write x3 everywhere instead of x.
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