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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

  • question_answer
    If\[\int\limits_{0}^{{{x}^{2}}}{f(t)}dt=x\cos \pi x,\]then the value of\[f(4)\]is:

    A)  \[1\]                    

    B)         \[\frac{1}{4}\]

    C)  \[-1\]                   

    D)         \[\frac{-1}{4}\]

    E)  \[-4\]

    Correct Answer: B

    Solution :

    \[\int\limits_{0}^{{{x}^{2}}}{f(t)}dt=x\cos \pi x\] On differentiating both sides, we get \[\therefore \] \[2xf({{x}^{2}})=\frac{-x\sin \pi x}{\pi }+\cos \pi x\] \[\Rightarrow \] \[{{x}^{2}}f{{(x)}^{2}}=-\frac{x\sin \pi x}{{{x}^{2}}\pi }+\frac{\cos \pi x}{{{x}^{2}}}\] \[\therefore \] \[f(4)=f({{2}^{2}})=\frac{1}{4}\]


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