-01sin -12 x -1-x2 dx -A- -2-2 log-2B- -2-2 log-2- -4-log-2D- -4-log-2

The correct option is A π/2 2 log √(2)Put x=tan θ, ∴ dx=sec^2 θ d θ As x=1 ⇒θ=π/4 and x=0⇒θ = 0, then I=2 ∫_0^π/4θ sec^2 θ d θ=2[θ tan θ]^π/4_0 2∫_0^π/4tan θ d ...

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Byju's Answer

Standard XII

Mathematics

Property 1

∫01sin -12 x ...

Question

$\int_{0}^{1} s i n^{- 1} (\frac{2 x}{1 + x^{2}}) d x =$

\frac{π}{2} - 2 l o g \sqrt{2}

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\frac{π}{2} + 2 l o g \sqrt{2}

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\frac{π}{4} - l o g \sqrt{2}

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\frac{π}{4} + l o g \sqrt{2}

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Solution

The correct option is A $\frac{π}{2} - 2 l o g \sqrt{2}$
$P u t x = t a n θ, ∴ d x = s e c^{2} θ d θ$
$A s x = 1 \Rightarrow θ = \frac{π}{4} a n d x = 0 \Rightarrow θ = 0, t h e n$
$I = 2 \int_{0}^{\frac{π}{4}} θ s e c^{2} θ d θ = 2 [θ t a n θ]_{0}^{\frac{π}{4}} - 2 \int_{0}^{\frac{π}{4}} t a n θ d θ$
$= \frac{π}{2} + 2 [l o g c o s x]_{0}^{\frac{π}{4}} = \frac{π}{4} - 2 l o g \sqrt{2}$

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