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JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    The value of \[\int\limits_{0}^{1}{\sqrt[3]{2{{x}^{3}}-3{{x}^{2}}-x+1}}\,dx\] is equal to

    A)  \[5\sqrt{7}\]                     

    B)  1

    C)  1                                            

    D)  \[2\sqrt{2}\]

    Correct Answer: C

    Solution :

    \[\because \,\,I=\int\limits_{0}^{1}{\sqrt[3]{2{{x}^{3}}-3{{x}^{2}}-x+1}}\] \[\Rightarrow \,I=\int\limits_{0}^{1}{\sqrt[3]{2{{(1-x)}^{3}}-3{{(1-x)}^{2}}-(1-x)+1}}\]\[\left( \because \,\int_{0}^{a}{f(x)dx=\int_{0}^{a}{f(a-x)dx}} \right)\] \[\Rightarrow \]\[I=\int\limits_{0}^{1}{\sqrt[3]{-2{{x}^{3}}+3{{x}^{2}}+x-1}}=-I\] \[\therefore \,\,2I=0\Rightarrow \,I=0\].


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