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KVPY Sample Paper KVPY Stream-SX Model Paper-16

  • question_answer
    \[\int\limits_{-1}^{1}{\frac{{{x}^{3}}+\left| \,x\, \right|+1}{{{x}^{2}}+2\left| \,x\, \right|+1}}\,\,dx=2\,\,\ell n2+b\] then

    A) \[a=2;~\,b=1\]

    B) \[a=2;\text{ }6=0\]

    C) \[a=3;\,~6=-\,2\]

    D) \[a=4;\,~b=-1\]

    Correct Answer: B

    Solution :

    \[I=\int\limits_{-1}^{1}{\frac{{{x}^{3}}}{{{x}^{2}}+2\left| \,x\, \right|+1}}\,\,dx+\int\limits_{-1}^{1}{\frac{\left| \,x\, \right|+1}{{{(\left| \,x\, \right|+1)}^{2}}}}\,\,dx\] \[=0+2\int\limits_{0}^{1}{\frac{dx}{1+x}}=2\ell n\,2\]


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