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Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications

Volume 2 , Issue 1 , PP: 33-43, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

A Study in the Integral of Sine and Cosine Functions

Maissam Jdid 1 * , Fatima Al Suleiman 2

  • 1 Faculty of Informatics Engineering, Al-Sham Private University, Damascus, Syria - (m.j.foit@aspu.edu.sy)
  • 2 Business Supervisor, Department of Mathematical, Faculty of Science, Damascus, Syria - (fatimasuliman2009@gmail.com)

    • Doi: https://doi.org/10.54216/GJMSA.020105

    Received: March 22, 2022 Accepted: July 27, 2022
    Abstract

    Trigonometric functions are among the most widely used functions in many science fields, especially sine and cosine functions because they are essential for periodic functions that describe sound and light waves in different types and wavelengths. Therefore, researchers studied the integrals of sine and cosine functions in different forms of the integrating function. In this paper, we spotlighted several most important yet under-studied integrals that are poorly mentioned in Arabic and foreign textbooks and studies. In addition, we studied Integral of Sine and Cosine for n as a positive rational number and concluded that each of these integrals leads to functional series. When studying the convergence of these series using the D'Alembert ratio test, we found that these series are convergent over the entire set of real numbers. This convergence is highly useful when applying such integrals in different science fields.

    Keywords :

    Power Series , Sine , Cosine , Convergence , Integral , D'Alembert Ratio Test.

    References

    [1] Vigodski - Translation by Dr. Anton Youssef Mansour - Reference in High Mathematics - Mir

    Publications- Moscow - 1975.

    [2] D. Gebran Gebran-D. Maissam Jdid - General Mathematics 3 - Damascus University Publications - 2015.

    [3] D. Ahmed Jallow - Business Supervisor Abdel Fattah Abbas – Calculus- Aleppo University - 2007.

    [4] Walter Ruden - Translation By D. Abdul-Samiyah Abdel-Razak Al-Jannani - Principles Of Mathematical

    Analysis - El-Muntasser University, Baghdad, 2002.

    [5] Teddy. Q. C. Levitt - Translation By A. D. Paul Simple Ruble - D. Magdi Mustafa Imam - D. Abdelatif

    Younis Muhyi - Terminations And Communication In Calculus - International Publishing And Distribution

    House - Cairo - 1989.

    [6] D. Frank Ayers-D. Robert Muir - Translation By M. Said Faraj Iskander - Dr. Intissarat Mohammed

    Hassan Al Haqqi - Triangle Account - International Cultural Investment House - Egypt – 2004

    [7] Mathematical Analysis And Applications. Switzerland, Mdpi Ag, 2019.

    [8] Zakon, Elias, Mathematical Analysis. The Trillia Group, 2009.

    [9] Zaidman, Samuel, Advanced Calculus-An Introduction To Mathematical Analysis. World Scientific

    Publishing Company, 1997.

    [10] Vladimir A.Zorich. Translator. Roger Cooke, Mathematical Analysis I. Burlington,Vermont,

    [11] Usa, 2004.

    [12] Thomas Calculus. International Edition –Pearson, 2013.

    [13] Ter-Krikorov, Aleksandr Murtynovich, Shabounnin Mikhailovich - Kurmathematical Analysis –

    [14] Ter_Krikorov A.M_ Shabunin M.N Of Mathematical Analysis_Bin. Laboratory Of Knowledge _2015

    [15] Y. G.Reshetnyak - Kursk Calculus Analysis 1 - Institute Of Mathematics Co Ron_1999

    [16] L. D. Kudryavtsev _ Short Course Of Mathematical Analysis Of Tom1_Fizmatlite _ _2015

    [17] A. M. Ter_ Cricorov, M. I. Shabunin Of Mathematical Analysis Laboratory Of Knowledge

    Vases_Moscow -2003

    [18] Vladimir A. Zorich. Translator. Roger Cooke - Mathematical Analysis Ii - Burlington, Vermont - Usa -

    2003

    [19] N. E. Zhukovsky And Y. A. Gagarin - Mathematical Analysis Of Examples And Problems _Vunz.

    Bbc_201

    Cite This Article As :
    Jdid, Maissam. , Al, Fatima. A Study in the Integral of Sine and Cosine Functions. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2022, pp. 33-43. DOI: https://doi.org/10.54216/GJMSA.020105
    Jdid, M. Al, F. (2022). A Study in the Integral of Sine and Cosine Functions. Galoitica: Journal of Mathematical Structures and Applications, (), 33-43. DOI: https://doi.org/10.54216/GJMSA.020105
    Jdid, Maissam. Al, Fatima. A Study in the Integral of Sine and Cosine Functions. Galoitica: Journal of Mathematical Structures and Applications , no. (2022): 33-43. DOI: https://doi.org/10.54216/GJMSA.020105
    Jdid, M. , Al, F. (2022) . A Study in the Integral of Sine and Cosine Functions. Galoitica: Journal of Mathematical Structures and Applications , () , 33-43 . DOI: https://doi.org/10.54216/GJMSA.020105
    Jdid M. , Al F. [2022]. A Study in the Integral of Sine and Cosine Functions. Galoitica: Journal of Mathematical Structures and Applications. (): 33-43. DOI: https://doi.org/10.54216/GJMSA.020105
    Jdid, M. Al, F. "A Study in the Integral of Sine and Cosine Functions," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 33-43, 2022. DOI: https://doi.org/10.54216/GJMSA.020105

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