JEE Main & Advanced Sample Paper JEE Main Sample Paper-41

  • question_answer
    If [.] denotes the greatest function, then the integral \[\int_{0}^{1.5}{[{{x}^{2}}]dx}\]equals

    A)  \[2-\sqrt{2}\]              

    B)  \[2+\sqrt{2}\]

    C)  \[\sqrt{2}\]                             

    D)  None of these

    Correct Answer: A

    Solution :

    \[\int_{0}^{1.5}{[{{x}^{2}}]dx}=\int_{0}^{1}{0dx}+\int_{1}^{\sqrt{2}}{1}dx\int_{\sqrt{2}}^{1.5}{2dx}\] \[=0+[x]_{1}^{\sqrt{2}}+2[x]_{\sqrt{2}}^{1.5}\] \[=\sqrt{2}-1+2(1.5-\sqrt{2})\] \[=2-\sqrt{2}\]


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