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J & K CET Engineering J and K - CET Engineering Solved Paper-2004

  • question_answer
    The value of \[\int_{0}^{\pi /2}{{{\sin }^{8}}\,x\,\,dx}\] is

    A)  \[\frac{105\,\pi }{32(4!)}\]

    B)  \[\frac{105\,\pi }{14\,(4!)}\]

    C)  \[\frac{105\,}{16\pi \,(4!)}\]

    D)  None of these

    Correct Answer: A

    Solution :

    Let \[I=\int_{0}^{\pi /2}{{{\sin }^{8}}x\,dx}\] Using gamma function \[=\frac{7.5.3.1}{8.6.4.2}.\,\frac{\pi }{2}\] \[=\frac{105\,\pi }{32(4.3.2.1)}\] \[=\frac{105\pi }{32.4!}\]


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