-11d-d xtan -11-x d x isA- -2B- -4C- -2D- -4

The correct options are C π/2 ∫_ 1^1d/dx ( tan^ 11/x )dx ∫_ 1^11/1+ ( 1/x )^2 ( 1/x^2 )dx = ∫_ 1^11/1+x^2dx = 2 ∫_0^1dx/1+x^2 (even function) = 2 [ tan^ 1x ...

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Byju's Answer

Standard XII

Mathematics

Inequalities of Integrals

∫-11d/d xtan ...

Question

$\int_{- 1}^{1} \frac{d}{d x} (t a n^{- 1} \frac{1}{x}) d x$ is

\frac{π}{2}

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\frac{π}{4}

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- \frac{π}{2}

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- \frac{π}{4}

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Solution

The correct option is C $- \frac{π}{2}$

$\int_{- 1}^{1} \frac{d}{d x} (t a n^{- 1} \frac{1}{x}) d x$
$\int_{- 1}^{1} \frac{1}{1 + {(\frac{1}{x})}^{2}} (\frac{- 1}{x^{2}}) d x = - \int_{- 1}^{1} \frac{1}{1 + x^{2}} d x = - 2 \int_{0}^{1} \frac{d x}{1 + x^{2}}$ (even function)
$= - 2 {[t a n^{- 1} x]}_{0}^{- 1} = - 2 \frac{π}{4} = - \frac{π}{2}$

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∫1−1ddx(tan−11x)dx is

The correct option is C −π2 ∫1−1ddx(tan−11x)dx ∫1−111+(1x)2(−1x2)dx=−∫1−111+x2dx=−2∫10dx1+x2 (even function) =−2[tan−1x]10=−2π4=−π2

$\int_{- 1}^{1} \frac{d}{d x} (t a n^{- 1} \frac{1}{x}) d x$ is