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Catalan's constant integration , Exams of Mathematics

Al-Aqsa UniversityMathematics

Catalan's constant integration

Typology: Exams

2016/2017

Uploaded on 10/18/2017

OSAMA-ALSATTARI
OSAMA-ALSATTARI 🇵🇸

4.6

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4 Evatuace: | In(cosx) dx 0 4 4 Solution: G = -| In(ttanx)dx = -| In(sinx) — In(cosx)dx 0 o 4 Hence, | ln(sinx) — In(cosx)dx = —G...(1) 0 Tw 4 1 fz 1 2 Also, [ In(sinx) + In(cosx)dx ... (2) = 5| In(sinx)dx + 5 | In(cosx) dx 0 0 0 Therefore, 5( —Fin(2) = sIn(2)] = — 5 In(2) As a L consequence, by solving (1), (2)we obtain 2" In(cosx)dx = 6 —F In(2) = (' In(cosx)dx = a(¢ -Fin(2)) MR. OSAMA A.A. ALSATTARI