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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    The value of\[\int_{-\pi /4}^{\pi /4}{{{x}^{3}}{{\sin }^{4}}x\,dx}\]is equal to:

    A)  \[\frac{\pi }{4}\]                                             

    B)  \[\frac{\pi }{2}\]

    C)  \[\frac{\pi }{8}\]                             

    D)         \[0\]

    E)  \[1\]

    Correct Answer: D

    Solution :

    Let \[I=\int_{-\pi /4}^{\pi /4}{{{x}^{3}}{{\sin }^{4}}x}\,dx\] Since,\[{{x}^{3}}si{{n}^{4}}x\]is an odd function. \[\therefore \] \[I=0\]


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