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JCECE Engineering JCECE Engineering Solved Paper-2009

  • question_answer
    \[\int_{-a}^{a}{x\sqrt{({{a}^{2}}-{{x}^{2}})}}dx\]is equal to

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

    B) \[\frac{\pi }{3}\]

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

    D) \[0\]

    Correct Answer: D

    Solution :

    Let          \[I=\int_{-a}^{a}{x}\sqrt{{{a}^{2}}-{{x}^{2}}}dx\] Let\[f(x)=x\sqrt{{{a}^{2}}-{{x}^{2}}}\] \[f(-x)=-x\sqrt{{{a}^{2}}-{{x}^{2}}}=-f(x)\] \[\therefore \]\[f(x)\]is an odd function. \[\therefore \]The value of given integral will be zero.


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