2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Definite Integration

JEE Main & Advanced Mathematics Definite Integration Question Bank Properties of Definite Integration

  • question_answer
    \[\int_{-\,\pi /2}^{\,\pi /2}{\,\frac{\sin x}{1+{{\cos }^{2}}x}{{e}^{-{{\cos }^{2}}x}}dx}\] is equal to              [AMU 1999]

    A)                 \[2{{e}^{-1}}\]  

    B)                 1

    C)                 0             

    D)                 None of these

    Correct Answer: C

    Solution :

               \[I=\int_{-\pi /2}^{\pi /2}{\frac{\sin x}{1+{{\cos }^{2}}x}{{e}^{-{{\cos }^{2}}x}}dx}\]                 \[\because \frac{\sin x}{1+{{\cos }^{2}}x}{{e}^{-{{\cos }^{2}}x}}\]is an odd function, \\[I=0\].


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