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KVPY Sample Paper KVPY Stream-SX Model Paper-28

  • question_answer
    If \[\int\limits_{-1}^{-4}{f\left( x \right)dx-4}\,\operatorname{and}\,\int\limits_{2}^{-4}{\left( 3-f\left( x \right) \right)dx=7}\]then the value \[\,\int\limits_{-2}^{1}{f\left( -x \right)dx}\]is

    A) 2

    B) \[-3\]

    C) 5

    D) none of these

    Correct Answer: D

    Solution :

    f\[\int\limits_{-1}^{-4}{f\left( x \right)dx=4}\operatorname{and}\int\limits_{2}^{-4}{\left( 3-f\left( x \right) \right)dx=7},\]\[\Rightarrow \int\limits_{-4}^{2}{f\left( x \right)dx=7+18=25}\]
    \[I=\int\limits_{-2}^{1}{f\left( -x \right)dx=\int\limits_{-1}^{2}{f\left( x \right)dx}}\]
    \[=\int\limits_{-1}^{-4}{f\left( x \right)+\int\limits_{-4}^{2}{f\left( x \right)dx=4+25}=29}\]


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