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1 ∫ 0 D D X { Sin − 1 ( 2 X 1 + X 2 ) } D X is Equal To(A) 0 (B) π (C) π/2 (D) π/4

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प्रश्न

\[\int\limits_0^1 \frac{d}{dx}\left\{ \sin^{- 1} \left( \frac{2x}{1 + x^2} \right) \right\} dx\] is equal to

विकल्प

  •  0

  •  π

  • π/2

  • π/4

MCQ
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उत्तर

π/2

\[\text{We have}, \]

\[I = \int_0^1 \frac{d}{dx}\left\{ \sin^{- 1} \left( \frac{2x}{1 + x^2} \right) \right\}dx\]

\[\text{We know since} \int f'(x) = f(x)\]

\[f(x) = si n^{- 1} \left( \frac{2x}{1 + x^2} \right) and f'(x) = \frac{d}{dx}\left\{ si n^{- 1} \left( \frac{2x}{1 + x^2} \right) \right\} \]

\[\text{Therefore}, I = \left[ \sin^{- 1} \left( \frac{2x}{1 + x^2} \right) \right]_0^1 \]

\[ = \sin^{- 1} \left( 1 \right) - \sin^{- 1} \left( 0 \right)\]

\[ = \frac{\pi}{2}\]

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अध्याय 19: Definite Integrals - MCQ [पृष्ठ १२०]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 19 Definite Integrals
MCQ | Q 33 | पृष्ठ १२०

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