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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

  • question_answer
    The value of  \[\int_{0}^{1}{\left[ 1-\frac{x}{1!}+\frac{{{x}^{2}}}{2!}-\frac{{{x}^{3}}}{3!}+...+\frac{{{(-1)}^{n}}{{x}^{n}}}{n!}+.... \right]}\] \[\times e{{x}^{2}}dx\]:

    A)  0                            

    B)         \[e-1\]

    C)  1                            

    D)         e

    E)  none of these

    Correct Answer: B

    Solution :

    \[\int_{0}^{1}{\left[ 1-\frac{x}{1!}+\frac{{{x}^{2}}}{2!}-\frac{{{x}^{3}}}{3!}+..... \right]}{{e}^{2x}}dx\] \[=\int_{0}^{1}{{{e}^{-x}}.}{{e}^{2x}}dx=[{{e}^{x}}]_{0}^{1}=e-1\]


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