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JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer
    The area enclosed by the curve\[y={{x}^{5}}\], the \[x-\]axis and the ordinates \[x=-1,\,\,x=1\] is

    A) \[0\]                                     

    B) \[\frac{1}{3}\]

    C) \[\frac{1}{6}\]                                   

    D)  None

    Correct Answer: B

    Solution :

     Required area                 \[=\int\limits_{-1}^{1}{|y|dx}=\int\limits_{-1}^{1}{|{{x}^{5}}|}\,dx=2\int\limits_{0}^{1}{|{{x}^{5}}|dx}\]                 \[=2\int\limits_{0}^{1}{{{x}^{5}}dx}=2\left[ \frac{{{x}^{6}}}{6} \right]_{0}^{1}=\frac{2}{6}=\frac{1}{3}\]


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