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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    If\[g(x)=\frac{f(x)-f(-x)}{2}\]defined over\[[-3,\text{ }3]\] and\[f(x)=2{{x}^{2}}-4x+1,\]then\[\int_{-3}^{3}{g(x)}dx\]is equal to:

    A)  0                                            

    B)  4

    C)  \[-4\]                   

    D)         8

    E)  none of these

    Correct Answer: A

    Solution :

    \[\because \] \[f(x)=2{{x}^{2}}-4x+1\] \[\therefore \] \[g(x)=\frac{2{{x}^{2}}-4x+1-2{{x}^{2}}-4x-1}{2}\] \[\Rightarrow \]               \[g(x)=-4x\] \[\therefore \]  \[\int_{-3}^{3}{g(x)}dx=-4\int_{-3}^{3}{x}\,dx\]                 \[=-4{{\left[ \frac{{{x}^{2}}}{2} \right]}^{3}}\]                 \[=-2[9-9]=0\]


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