-11d-d xtan -11-x d x

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

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

∫-11d/d xtan ...

Question

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

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Solution

The correct option is C

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

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1∫−1ddx(tan−11x) dx

The correct option is C 1∫−1ddx(tan−11x) dx==1∫−111+(1x)2(−1x2) dx=−1∫−1dx1+x2=−21∫0dx1+x2 (An even function)=−2[tan−1 x]10=−2π4=−π2

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