{ (( Ω_1 = ∫_0 ^( (π/2)) (( x^( 2) )/(sin^( 2) (x))) dx )),(( ⇒ (Ω_1 /Ω_( 2) ) = ? )),(( Ω_( 2) = ∫


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Question Number 195846 by mnjuly1970 last updated on 11/Aug/23
${ (( Ω_1 = ∫_0 ^( (π/2)) (( x^( 2) )/(sin^( 2) (x))) dx )),(( ⇒ (Ω_1 /Ω_( 2) ) = ? )),(( Ω_( 2) = ∫_0 ^( (π/2)) (x/(tan(x))) dx)) :}$
${\begin{cases} Ω_{1} = \int_{0}^{\frac{π}{2}} \frac{x^{2}}{{s i n}^{2} (x)} d x \\ \Rightarrow \frac{Ω_{1}}{Ω_{2}} = ? \\ Ω_{2} = \int_{0}^{\frac{π}{2}} \frac{x}{t a n (x)} d x \end{cases}$
	Answered by sniper237 last updated on 11/Aug/23

	$b y p a r t s i n t e g r a t i o n Ω_{2} = \frac{1}{2} Ω_{1}$
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