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JCECE Engineering JCECE Engineering Solved Paper-2012

  • question_answer
    If \[f(x)\] is an even function, then\[\int_{0}^{x}{f(t)}\,\,dt\]

    A)  odd function

    B)  even function

    C)  neither even nor odd

    D)  None of the above

    Correct Answer: A

    Solution :

    Let\[\phi (x)=\int_{0}^{x}{(t)dt}\], \[\phi (-x)=\int_{0}^{-x}{f(t)}dt=-\int_{0}^{x}{f(-2)dz}\]                                 (putting\[t=-z\Rightarrow dt=-dz)\]                 \[=-\int_{0}^{x}{f(t)}dt=\phi (x)\] \[\therefore \,\,\phi (x)\]is an odd function.


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