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BCECE Engineering BCECE Engineering Solved Paper-2008

  • question_answer
    The value of \[\int_{-\pi /2}^{\pi /2}{\log \left( \frac{2-\sin \theta }{2+\sin \theta } \right)}d\theta \]is

    A)  0                            

    B)         1                            

    C)         2                            

    D)         None of these

    Correct Answer: A

    Solution :

    Let \[\int_{-\pi /2}^{\pi /2}{\log \left( \frac{2-\sin \theta }{2+\sin \theta } \right)}d\theta \] Again let \[f(-\theta )=\log \left( \frac{2-\sin \theta }{2+\sin \theta } \right)\] Now,\[f(-\theta )=log\left( \frac{2+\sin \theta }{2-\sin \theta } \right)\] \[=-\log \left( \frac{2-\sin \theta }{2+\sin \theta } \right)=-f(\theta )\] \[\therefore \]\[f(\theta )\]is an odd function \[\therefore \]  \[I=0\]


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