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1 ∫ 0 √ 1 − X 1 + X D X

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Question

\[\int\limits_0^1 \sqrt{\frac{1 - x}{1 + x}} dx\]

Sum
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Solution

\[\int_0^1 \sqrt{\frac{1 - x}{1 + x}} d x\]

\[ = \int_0^1 \sqrt{\frac{1 - x}{1 + x} \times \frac{1 - x}{1 - x}} d x\]

\[ = \int_0^1 \frac{1 - x}{\sqrt{1 - x^2}} d x\]

\[ = \int_0^1 \frac{1}{\sqrt{1 - x^2}}dx - \int_0^1 \frac{x}{\sqrt{1 - x^2}}dx\]

\[ = \left[ \sin^{- 1} x \right]_0^1 + \left[ \sqrt{1 - x^2} \right]_0^1 \]

\[ = \frac{\pi}{2} - 1\]

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Chapter 19: Definite Integrals - Revision Exercise [Page 121]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 19 Definite Integrals
Revision Exercise | Q 17 | Page 121

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