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J & K CET Engineering J and K - CET Engineering Solved Paper-2008

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

    A)  \[0\]

    B)  \[1\]

    C)  \[2\]

    D)  \[3\]

    Correct Answer: C

    Solution :

    Let   \[I=\int_{-\pi /2}^{\pi /2}{\frac{dx}{2\,{{\cos }^{2}}\frac{x}{2}}}\] \[=\int_{0}^{\pi /2}{{{\sec }^{2}}\frac{x}{2}dx}\] \[=\left[ 2\,\,\tan \frac{x}{2} \right]_{0}^{\pi /2}=2\]


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