2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Indefinite Integrals

JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    The value of \[\int_{{}}^{{}}{\frac{dx}{\sqrt{1-x}}}\] is [Pb. CET 2001]

    A)            \[2\sqrt{1-x}+c\]

    B)            \[-2\sqrt{1-x}+c\]

    C)            \[-{{\sin }^{-1}}\sqrt{x}+c\]

    D)             \[{{\sin }^{-1}}\sqrt{x}+c\]

    Correct Answer: B

    Solution :

               We have, \[\int_{{}}^{{}}{\frac{dx}{\sqrt{1-x}}}\] or \[I=\int_{{}}^{{}}{{{(1-x)}^{-1/2}}dx}\]            \[I=\frac{{{(1-x)}^{\frac{-1}{2}+1}}}{(-1)\,\left( -\frac{1}{2}+1 \right)}+c\] Þ \[I=-2\sqrt{1-x}+c\].


You need to login to perform this action.
You will be redirected in 3 sec spinner