9. The value of the integraiſ (a) I...
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9. The value of the integraiſ (a) II 02-1 (0-1 dris

JEE/Engineering Exams
Maths
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( begin{aligned} I &=int_{0}^{1} sqrt{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}}} d x-int_{0}^{1} frac{x}{sqrt{1-x^{2}}} d x &=left[sin ^{-1} xright]_{0}^{1}+int_{1}^{0} frac{t}{t} d t &=left(sin ^{-1} 1-sin ^{-1} 0right)+[t]_{1}^{0}=pi / 2-1 end{aligned} )
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