2. Solved Papers
  3. J & K CET Engineering

J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    The     value     of     the     integral \[\int_{-\pi /2}^{\pi /2}{\sqrt{1-{{\cos }^{2}}\theta }}\,\,d\theta \]is equal to

    A)  \[0\]                 

    B)  \[1\]

    C)  \[2\]                 

    D)  \[-2\]

    Correct Answer: C

    Solution :

    Let \[I=\int_{-\pi /2}^{\pi /2}{\sqrt{1-{{\cos }^{2}}\theta }\,d\theta }\] \[=\int_{-\pi /2}^{\pi /2}{|\sin \theta |\,\,d\theta }\] \[=2\int_{0}^{\pi /2}{\sin \theta \,\,\,d\theta }\] \[=2[-\cos \,\theta ]_{0}^{\pi /2}\] \[=2\left( -\cos \frac{\pi }{2}+\cos \,{{0}^{o}} \right)\] \[=2(1)=2\]


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