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J & K CET Engineering J and K - CET Engineering Solved Paper-2007

  • question_answer
    \[\int_{0}^{\pi }{{{\cos }^{3}}\,x\,\,dx}\]is equal to

    A)  \[0\]

    B)  \[1\]

    C)  \[-1\]

    D)  \[\frac{1}{2\sqrt{2}}\]

    Correct Answer: A

    Solution :

    Let  \[I=\int_{0}^{\pi }{{{\cos }^{3}}\,\,x\,\,dx}\] ?.(i) \[=\int_{0}^{\pi }{{{\cos }^{3}}\,\,(\pi -x)\,\,dx}\] \[\Rightarrow \] \[I=-\int_{0}^{\pi }{{{\cos }^{3}}\,x\,dx}\] ??(ii) On adding Eqs. (i) and (ii), we get \[2I=0\] \[\Rightarrow \] \[I=0\]


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