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JEE Main & Advanced Mathematics Definite Integration Question Bank Fundamental definite integration, Definite integration by substitution

  • question_answer
    The value of \[\int_{0}^{1}{{{x}^{2}}{{e}^{x}}dx}\]is equal to       [Pb. CET 2002]

    A)                 \[e-2\] 

    B)                 \[e+2\]

    C)                 \[{{e}^{2}}-2\]  

    D)                 \[{{e}^{2}}\]

    Correct Answer: A

    Solution :

               We have, \[I=\int_{0}^{1}{{{x}^{2}}{{e}^{x}}dx}\]Þ \[I=[{{x}^{2}}.{{e}^{x}}]_{0}^{1}-\int_{0}^{1}{2x.{{e}^{x}}dx}\]                    Þ \[I=e-2[x{{e}^{x}}-{{e}^{x}}]_{0}^{1}\]Þ\[I=e-2\,[e-e-(0-1)]\]                                 Þ  \[I=e-2\].


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