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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    If\[\int_{a}^{b}{{{x}^{3}}}dx=0\]and\[\int_{a}^{b}{{{x}^{2}}}dx=\frac{2}{3},\]then the values of a and b are respectively

    A)  \[1,-1\]               

    B)         \[-1,1\]

    C)  \[1,1\]                 

    D)         \[-1,-1\]

    E)  \[1,0\]

    Correct Answer: B

    Solution :

    Since,\[\int_{a}^{b}{{{x}^{3}}}dx=0\]and \[\int_{a}^{b}{{{x}^{2}}}dx=\frac{2}{3}\] \[\therefore \] \[\left[ \frac{{{x}^{4}}}{4} \right]_{a}^{b}=0\]amd \[\left[ \frac{{{x}^{3}}}{3} \right]_{a}^{b}=\frac{2}{3}\] \[\Rightarrow \] \[{{b}^{4}}-{{a}^{4}}=0\]and \[{{b}^{3}}-{{a}^{3}}=2\] \[\Rightarrow \] \[a=-1,b=1\]


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