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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Self Evaluation Test - Integrals

  • question_answer
    Let\[f(x)=\int{{{e}^{x}}(x-1)(x-2)}dx\]. Then f decreases in the interval

    A) \[(-\infty ,-2)\]

    B) \[(-2,-1)\]

    C) \[(1,\,\,2)\]

    D) \[(2,+\infty )\]

    Correct Answer: C

    Solution :

    [c] \[f(x)=\int{{{e}^{x}}(x-1)(x-2)dx}\] For decreasing function, \[f'(x)<0\] \[\Rightarrow {{e}^{x}}(x-1)(x-2)<0\] \[\Rightarrow (x-1)(x-2)<0\] \[\Rightarrow 1<x<2\] \[\therefore {{e}^{x}}>0\forall x\in R\]


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