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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

  • question_answer
    If\[\int_{-1}^{4}{f(x)}dx=4\]and\[\int_{2}^{4}{[3-f(x)]}dx=7,\]then the value of\[\int_{-1}^{2}{f(x)}\,dx\]is:

    A)  \[-2\]                   

    B)         3

    C)  5                            

    D)         8

    E)  \[-1\]

    Correct Answer: C

    Solution :

    \[\int_{2}^{4}{[3-f(x)]}\,dx=7\] \[\Rightarrow \]               \[[3x]_{2}^{4}-\int_{2}^{4}{f(x)}\,dx=7\] \[\Rightarrow \]               \[6-\int_{2}^{4}{f(x)}\,dx=7\] \[\Rightarrow \]               \[\int_{2}^{4}{f(x)}\,dx=-1\]                                           ...(i) and            \[\int_{-1}^{4}{f(x)}\,dx=4\]                      ...(ii) \[\int_{-1}^{4}{f(x)}\,dx=\int_{-1}^{2}{f(x)}\,dx+\int_{2}^{4}{f(x)}\,dx\]               \[\Rightarrow \]               \[4=\int_{-1}^{2}{f(x)}\,dx-1\] \[\Rightarrow \]               \[=\int_{-1}^{2}{f(x)}\,dx=5\]


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