prove that I= ∫_0 ^( (π/2)) ln ( 1+ sin (2 α )) dα = 2G − π ln ((√2) ) G: catalan constant


Question and Answers Forum

All Questions Topic List
Integration Questions
Previous in All Question Next in All Question
Previous in Integration Next in Integration
Question Number 161089 by mnjuly1970 last updated on 12/Dec/21

$p r o v e t h a t$ $I = \int_{0}^{\frac{π}{2}} \ln (1 + s i n (2 α)) d α$ $= 2 G - π \ln (\sqrt{2})$ $G : c a t a l a n c o n s t a n t$
	Answered by Ar Brandon last updated on 11/Dec/21

	$I = \int_{0}^{\frac{π}{2}} \ln (1 + \sin 2 α) d α$ $= \int_{0}^{\frac{π}{2}} \ln {(\cos α + \sin α)}^{2} d α$ $= 2 \int_{0}^{\frac{π}{2}} \ln (\cos α + \sin α) d α$ $= 2 (G - \frac{π \ln 2}{4}) = 2 G - \frac{π \ln 2}{2}$ $= 2 G - π \ln \sqrt{2}$
	Answered by mnjuly1970 last updated on 12/Dec/21

	Commented by Tawa11 last updated on 12/Dec/21

	$Great sir$
	Answered by mnjuly1970 last updated on 12/Dec/21

Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum